Free NEET Physics multiple-choice questions on Vectors & Operations. Attempt each question and reveal the answer with a full explanation.
A particle moves with a velocity v = 5 i + 2 j . The angle made by the velocity vector with the y-axis is: -1 (2.5) -1 (0.4) -1 (0.4) -1 (0.4) The unit vector along i + j is: ( i + j ) / 2 i + j ( i + j ) / 2 ( i - j ) / 2 If a vector A has a magnitude of 5 and is directed towards the North, and vector B has a magnitude of 5 and is directed towards the East, then the direction of ( A - B ) is: North-West North-East South-West South-East A vector P is such that it makes equal angles with the x, y and z axes. The component of a unit vector along P along any of the axes is: 1/ 3 1/3 1/ 2 3 Two vectors A and B are defined as A = 2 i + 3 j and B = i + j . The component of A along the direction of B is: 5/ 2 5 2/ 5 13 If the sum of two vectors A and B is perpendicular to their difference, then: |A| = |B| A is perpendicular to B A is parallel to B A dot B = 1 A particle starting from the origin (0,0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are ( 3 , 3) . The path of the particle makes with the x -axis an angle of: 60 30 45 0 If the magnitude of the vector product of two vectors is 3 times the scalar product of the two vectors, the angle between the two vectors is: 60 30 45 90 The unit vector in the direction of vector A = 2 i + 3 j + k is: 2 i + 3 j + k 14 2 i + 3 j + k 6 2 i + 3 j + k 14 i + j + k The angle between vectors A = i + j and B = i - j is: 90 45 0 180 A vector A makes equal angles with the x, y and z axes. If its magnitude is 10 3 , its component along the y -axis is: 10 10 3 5 3 20 Vector A has magnitude 2 and vector B has magnitude 3 . If A B = 0 , then the magnitude of A B is: 6 0 13 1 If the angle between vectors A and B is 60 , the ratio of A B to | A B | is: 1 3 3 1 1 2 If | A B | = A B , then the angle between A and B is: 45 30 60 90 If the magnitude of the sum of two vectors of equal magnitude is equal to the magnitude of either vector, then the angle between the two vectors is: 120 60 90 180 The angle between the vectors ( A B ) and ( B A ) is: /2 0 /4 A particle has an initial velocity of 3 i + 4 j and an acceleration of 0.4 i + 0.3 j . Its speed after 10 s is: 7 2 units 7 units 8.5 units 10 units The scalar product of two vectors is 2 3 and the magnitude of their vector product is 2 . The angle between the two vectors is: 30 60 45 90 A vector A has magnitude A and n is a unit vector in the direction of A , then: n = A /A n = A A n = A/ A n = A A Two vectors A and B have magnitudes 3 and 4 units respectively. What is the angle between them if the magnitude of their cross product is 6 units? 30 60 45 0 The vectors A and B are such that | A + B | = | A | + | B | . The angle between the vectors A and B is: 0 60 90 180 Two vectors A and B are such that | A + B | = | A - B | . The angle between the two vectors is: 90 60 0 180 If the dot product of two non-zero vectors A and B is equal to -| A || B | , then the angle between the vectors is: /2 0 /4 If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is: 90 45 180 0 If the magnitude of the sum of two vectors is equal to the magnitude of either of the vectors, then the angle between the two vectors is: 120 90 60 0 The component of vector A = 2 i + 3 j along the direction of ( i + j ) is: 5/ 2 5 13 1/ 2 The angle between ( i + j + k ) and ( i - j ) is: 90 45 0 60 If the scalar and vector products of two vectors A and B are equal in magnitude, then the angle between them is: 45 90 180 30 If the magnitude of the cross product of two vectors is equal to their dot product, the angle between the two vectors is: 45 30 60 90 The unit vector parallel to the resultant of the vectors A = 4 i + 3 j + 6 k and B = - i + 3 j - 8 k is: 1 7 (3 i + 6 j - 2 k ) 1 7 (3 i + 6 j + 2 k ) 1 49 (3 i + 6 j - 2 k ) 1 31 (3 i + 6 j - 2 k ) If the angle between A and B is , then | A B | 2 + ( A B ) 2 is equal to: A 2 B 2 A 2 + B 2 (A+B) 2 zero If a vector 2 i + 4 j - 5 k is perpendicular to λ i + 2 j + 3 k , the value of λ is: 3.5 -3.5 7 -7 The unit vector in the direction of the vector A = i + j + k is: ( i + j + k ) / √3 ( i + j + k ) / 3 √3( i + j + k ) ( i + j + k ) A person walks 4 m North, then 3 m East and finally 12 m vertically upwards. The magnitude of the total displacement from the starting point is: 13 m 19 m 5 m 12 m A vector F has magnitude 10 N and makes an angle of 30 with the y -axis. Its component along the x -axis is: 5 N 5√3 N 10 N 0 N A vector A = 3 i + 4 j + 5 k makes an angle α with the x -axis. The value of cos α is: 3 / 5√2 3/5 4/5 1/√2 The angle between the vectors A = i + j and B = j + k is: 60 30 45 90 A vector A has magnitude 5 units and points North. Vector B has magnitude 5 units and points East. The magnitude and direction of A - B is: 5 2 units, North-West 5 2 units, North-East 10 units, North-West 0 units, No direction A particle has an initial velocity 3 i + 4 j and an acceleration 0.4 i + 0.3 j . Its speed after 10s is: 7 2 units 7 units 8.5 units 10 units If a vector A makes angles , , with x, y, z axes respectively, then 2 + 2 + 2 is: 1 0 -1 2 Two vectors a and b are such that | a + b | = | a - b | . The angle between them is: 90 0 60 180 The unit vector parallel to the vector A = 3 i + 4 j - 2 k is: 3 i + 4 j - 2 k 29 3 i + 4 j - 2 k 5 3 i + 4 j - 2 k 29 3 i + 4 j - 2 k 9 For angles of projection of a projectile at angles (45 - ) and (45 + ) , the horizontal ranges described by the projectile are in the ratio of: 1 : 1 2 : 3 1 : 2 2 : 1 A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are ( 3 , 3) . The path of the particle makes with the x-axis an angle of 45° 60° 0° 30° If the magnitude of the sum of two non-zero vectors A and B is equal to the magnitude of their difference, then the vectors A and B must be: Perpendicular to each other Parallel to each other Anti-parallel to each other Equal in magnitude The velocity of a projectile at the initial point A is (2 i +3 j ) m/s. Its velocity (in m/s) at point B is -2 i -3 j -2 i +3 j 2 i -3 j 2 i +3 j A particle moves so that its position vector is given by r = t , x + t , y . Where is a constant. Which of the following is true ? Velocity and acceleration both are perpendicular to r . Velocity and acceleration both are parallel to r Velocity is perpendicular to r and acceleration is directed towards the origin Velocity is perpendicular to r and acceleration is directed away from the origin A ball of mass 1 kg is thrown vertically upwards and returns to the ground after 3 seconds. Another ball, thrown at 60 with vertical also stays in air for the same time before it touches the ground. The ratio of the two heights are 1 : 3 1 : 2 1 : 1 2 : 1 A car starts from rest and accelerates at 5 m/s 2 . At t = 4 s , a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s ? (Take g = 10 m/s 2 ) 20 m/s, 0 20 2 m/s, 0 20 2 m/s, 10 m/s 2 20 m/s, 5 m/s 2 A ball is projected with a velocity, 10 ms -1 , at an angle of 60 with the vertical direction. Its speed at the highest point of its trajectory will be 5 3 ms -1 5 ms -1 10 ms -1 Zero A bullet is fired from a gun at the speed of 280 m s -1 in the direction 30 above the horizontal. The maximum height attained by the bullet is (g = 9.8 m s -2 , 30 = 0.5) 2800 m 2000 m 1000 m 3000 m A particle has initial velocity (2 + 3) and acceleration (0.3 + 0.2) . The magnitude of velocity after 10 seconds will be: 5√2 units 9 units 5 units 10 units If a vector 2 + 3 + 8 is perpendicular to the vector 4 - 4 + α , then the value of α is: -1/2 1/2 1 -1 The angle between A and B is . The value of the triple product A ( B A ) is: Zero A 2B A 2B θ A 2B θ Two vectors A and B have equal magnitudes. If magnitude of ( A + B ) is equal to n times the magnitude of ( A - B ) , then the angle between A and B is: -1 ((n 2-1)/(n 2+1)) -1 ((n-1)/(n+1)) -1 ((n 2-1)/(n 2+1)) -1 (n 2-1) A vector A is along the positive z -axis. The value of A ( i j ) is: A 0 1 -A The unit vector perpendicular to both A = 2 i + 3 j + k and B = i - j + 2 k is: 1 75 (7 i - 3 j - 5 k ) 1 75 (7 i + 3 j + 5 k ) 1 59 (3 i - 5 j - 7 k ) 1 59 (7 i - 3 j + 5 k ) If the angle between the vectors A and B is , the value of the product ( B A ) A is equal to: Zero BA 2 BA 2 BA 2 A vector P makes angles , and with the x, y and z axes respectively. Then 2 + 2 + 2 is equal to: 2 1 0 3 Two vectors are given by A = 3 i + j + 2 k and B = 2 i - 2 j + 4 k . The value of | A B | is: 8 3 8 10 5 2 A vector A points vertically upward and B points towards north. The vector product A B is: Along West Along East Along South Zero A vector P is rotated through a small angle d without changing its magnitude. The magnitude of the change in vector d P is: P d 0 P P/d The area of a parallelogram whose adjacent sides are represented by the vectors A = 3 i + j + 4 k and B = i - j + k is: 42 32 50 10 If a vector A has magnitude 10 and makes an angle of 60 with the x-axis, and vector B has magnitude 10 and makes an angle of 120 with the x-axis, the magnitude of A + B is: 10 3 20 10 0 If the sum of two unit vectors is also a unit vector, then the magnitude of their difference is: 3 2 1 2 A bullet is fired from a gun. The force on the bullet is given by F = 600 - 2 10 5 t where F is in Newtons and t is in seconds. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet? 0.9 Ns 1.8 Ns 0.45 Ns 9 Ns If a vector A of magnitude 10 units is added to a vector B of magnitude 6 units, the magnitude of the resultant vector can never be: 3 units 4 units 10 units 16 units The unit vector in the direction of the sum of vectors A = 2 i + 2 j and B = 2 i + 2 k is: 2 i + j + k 6 i + j + k 3 4 i + 2 j + 2 k 24 i + j + k 3 Find the angle that the vector A = i + j + 2 k makes with the z -axis. 45 30 60 90 If | A B | = | A B | , then the magnitude of | A + B | is: (A 2 + B 2 + 2 AB) 1/2 (A 2 + B 2 + AB) 1/2 A+B (A 2 + B 2) 1/2 The angle made by vector A = i + j + 2 k with the z -axis is: 45 30 60 90 Two vectors A and B are such that | A + B | = | A | - | B | . This condition is satisfied when: The vectors are anti-parallel and A B The vectors are parallel The vectors are perpendicular The angle between them is 60 A vector A makes equal angles with x, y and z axes. The value of its direction cosines is: 1/ 3 1/2 3 /2 1/ 2 The component of a vector r = 2 i + 3 j along the direction ( i - j ) is: -1/ 2 1/ 2 5/ 2 -5/ 2 Two boys are standing at the ends A and B of a ground where AB = a . The boy at B starts. running in a direction perpendicular to AB with velocity v 1 . The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is - a v 2+v 1 2 a 2 v 2-v 1 2 a (v-v 1) a (v+v 1) A projectile is fired from the surface of the earth with a velocity of 5 ms -1 and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 ms -1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in ms -2 ) given g = 9.8 m/s 2 3.5 5.9 16.3 110.8 The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t. north is given by : 45° west 30° west 0° 60° west A vector A has components A x = 3, A y = 4, A z = 0 . The angle made by this vector with the x -axis is: -1 (0.6) -1 (0.6) -1 (0.75) 37 A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' ' to the horizontal, the maximum height attained by it equals 4R . The angle of projection, , is then given by : = -1 ( 2R gT 2 ) 1/2 = -1 ( 2R gT 2 ) 1/2 = -1 ( 2gT 2 2R ) 1/2 = -1 ( gT 2 2R ) 1/2 Two vectors P and Q are such that | P + Q | = | P | . This implies that: The angle between P and Q is obtuse Q must be zero P and Q are parallel The angle between P and Q is acute If the position vector of a particle is r = (t 2 - 4t + 6) i + (t 2) j , the time at which the velocity vector is perpendicular to the acceleration vector is: 1 s 2 s 3 s 0 s The resultant of two vectors P and Q is of magnitude P . If the vector P is doubled, the new resultant becomes perpendicular to Q . The angle between P and Q is: 120 60 150 90 Two vectors a and b are such that | a + b | = | a | . If a is perpendicular to (2 a + b ) , then the angle between a and b is: 120 60 90 150 Two vectors P and Q have equal magnitudes. If magnitude of ( P + Q ) is n times the magnitude of ( P - Q ) , then the angle between P and Q is: 2 -1 ( 1 n ) -1 ( n 2-1 n 2+1 ) -1 ( 1-n 2 1+n 2 ) -1 (n) What is the projection of vector A = 2 i + 3 j on the y -axis? 3 2 13 5