MOTION IN A PLANE

Which of the following quantities is a scalar? A) Velocity B) Force C) Temperature D) Displacement
Which of the following is a vector quantity? A) Mass B) Time C) Distance D) Acceleration
Which of the following is a scalar quantity? A) Momentum B) Speed C) Displacement D) Acceleration
Which of the following is a vector quantity? A) Pressure B) Energy C) Work D) Electric field
Which of the following is a scalar quantity? A) Electric field B) Force C) Magnetic field D) Displacement

Two particles A and B have position vectors r_A = (3i⃗ - 4j⃗) and r_B = (2i⃗ + 5j⃗). What is the displacement vector from A to B? A) (5i⃗ + 9j⃗) B) (-1i⃗ + 9j⃗) C) (1i⃗ - 9j⃗) D) (-5i⃗ - 9j⃗)
Which of the following is true for the displacement vector of a particle? A) It is always zero. B) It can be negative. C) It is always perpendicular to the position vector. D) It has no direction.
A particle moves from point A to point B along a straight line. What is the displacement vector from A to B? A) It depends on the path taken. B) It is always zero. C) It is always perpendicular to the line AB. D) It is directed from A to B.
The displacement vector of a particle is given by Δr⃗ = (-3i⃗ + 4j⃗). What is the final position of the particle if its initial position is at the origin? A) (3, -4) B) (-3, 4) C) (-3, -4) D) (4, -3)

Which notation represents a vector quantity? A) m B) s C) p D) v⃗
Which of the following is a scalar quantity? A) F⃗ B) G⃗ C) R⃗ D) V⃗
Which notation is used for a general vector in physics? A) v⃗ B) V⃗ C) v D) V
Which of the following is a vector quantity? A) Tension B) Pressure C) Energy D) Power

Two vectors A⃗ and B⃗ are equal if: A) They have the same magnitude only. B) They have the same direction only. C) They have the same magnitude and direction. D) They have opposite directions.
If vector A⃗ = (3i⃗ + 2j⃗) and vector B⃗ = (2i⃗ + 3j⃗), are they equal? A) Yes B) No
Two vectors are equal if and only if: A) They have the same magnitude. B) They have the same direction. C) They have the same magnitude and direction. D) They have the same magnitude, direction, and sense.
Two vectors A⃗ and B⃗ are given by A⃗ = (3i⃗ - 2j⃗) and B⃗ = (-3i⃗ + 2j⃗). Are they equal? A) Yes B) No
Two vectors A⃗ and B⃗ are equal if their components along the x and y directions are equal. Is this statement true or false? A) True B) False

Addition and Subtraction of Vectors:

Which of the following is not true for vector addition? A) The order of addition matters. B) It follows the commutative law. C) It follows the associative law. D) The result is independent of the choice of the coordinate system.
The sum of two vectors A⃗ and B⃗ is given by R⃗ = A⃗ + B⃗. If the magnitude of A⃗ is 5 units and the magnitude of B⃗ is 3 units, what is the maximum possible magnitude of R⃗? A) 2 units B) 3 units C) 5 units D) 8 units
The resultant of vector addition is maximum when the angle between the vectors being added is: A) 0° B) 45° C) 90° D) 180°
Two vectors A⃗ and B⃗ are given by A⃗ = (3i⃗ + 2j⃗) and B⃗ = (-2i⃗ + 3j⃗). What is the magnitude of their sum? A) 1 B) 2 C) 3 D) 5

Relative velocity is the velocity of an object or observer: A) Measured with respect to the Earth's surface. B) Measured in a moving frame of reference. C) Measured relative to the speed of light. D) Measured relative to the speed of sound.
Two cars A and B are moving in the same direction. Car A is moving at 50 km/h, and car B is moving at 60 km/h. What is the relative velocity of car B with respect to car A? A) 10 km/h B) 50 km/h C) 60 km/h D) 110 km/h
Two objects are moving in the same direction. Object A is moving at a speed of 10 m/s, and object B is moving at a speed of 15 m/s. What is the relative velocity of object B with respect to object A? A) 5 m/s B) 10 m/s C) 15 m/s D) 25 m/s
Two boats are moving perpendicular to each other. Boat A is moving at a speed of 5 m/s east, and boat B is moving at a speed of 8 m/s north. What is the relative velocity of boat B with respect to boat A? A) 5 m/s B) 8 m/s C) 9 m/s D) 13 m/s
Two trains are moving in opposite directions. Train A is moving at a speed of 100 km/h, and train B is moving at a speed of 120 km/h. What is the relative velocity of train B with respect to train A?
A) 20 km/h B) 100 km/h C) 120 km/h D) 220 km/h

A unit vector has a magnitude of: A) 0 B) 1 C) 10 D) -1
Which of the following is a unit vector? A) i⃗ B) j⃗ C) k⃗ D) All of the above
Which of the following vectors is a unit vector? A) (1, 0) B) (0, 1) C) (1, 1) D) (2, 2)
Which of the following is a unit vector in the y-direction? A) i⃗ B) j⃗ C) k⃗ D) -j⃗
Which of the following vectors is a unit vector in the x-direction? A) i⃗ B) j⃗ C) k⃗ D) -i⃗
Resolution of a Vector in a Plane:
The resolution of a vector in a plane involves breaking it down into its components along: A) X-axis only B) Y-axis only C) Both X-axis and Y-axis D) Z-axis
A vector has components A_x = 4 and A_y = 3. What is the magnitude of the vector? A) 4 B) 3 C) 5 D) 7
A vector has components A_x = -5 and A_y = 12. What is the angle it makes with the positive x-axis? A) 30° B) 45° C) 60° D) 90°
A vector has components A_x = 3 and A_y = -4. What is the angle it makes with the positive x-axis? A) 30° B) 45° C) 60° D) 90°
A vector has components A_x = 2 and A_y = 2. What is the angle it makes with the positive x-axis? A) 30° B) 45° C) 60° D) 90°

What are the rectangular components of a vector with a magnitude of 10 units and an angle of 30° with the x-axis? A) (5, 5) B) (10, 0) C) (5√3, 5) D) (10√3, 0)
A vector has components A_x = 3 and A_y = -4. What are its rectangular components? A) (3, -4) B) (-3, 4) C) (4, -3) D) (-4, 3)
A vector has rectangular components (6, 8). What is its magnitude? A) 2 B) 10 C) 36 D) 64
A vector has rectangular components (5, -12). What is the angle it makes with the positive x-axis? A) 30° B) 45° C) 60° D) 90°
A vector has rectangular components (3, -4). What is the angle it makes with the positive y-axis? A) 30° B) 45° C) 60° D) 90°

Scalar and Vector Product of Two Vectors:
The scalar product of two perpendicular vectors is: A) Zero B) Positive C) Negative D) Indeterminate
The vector product of two parallel vectors is: A) Zero B) Positive C) Negative D) Indeterminate
Which of the following is not true for the scalar product of two vectors? A) It is commutative. B) It is distributive. C) It gives a scalar result. D) It depends on the choice of the coordinate system.
The scalar product of two vectors A⃗ and B⃗ is given by A⃗ · B⃗. If the magnitude of A⃗ is 5 units and the magnitude of B⃗ is 3 units, what is the maximum possible value of the scalar product? A) 2 units B) 3 units C) 5 units D) 8 units
The vector product of two vectors A⃗ and B⃗ is given by A⃗ × B⃗. If the magnitude of A⃗ is 5 units and the magnitude of B⃗ is 3 units, what is the maximum possible value of the vector product? A) 2 units B) 3 units C) 5 units D) 8 units

Vector Algebra (MCQ FOR JEE AND GUJCET)