Vectors MCQs with Answers

Ans. The correct answer is d. \(\vec{A}\)

Explanation: The vector A can be represented by an arrow over the symbol A i.e. \(\vec{A}\)

Ans. The correct answer is d. 2, 3

Explanation: The given equation is 2i + 3j = xi + yj

On comparing the two equations, we get

x = 2 and y = 3

Ans. The correct answer is a. -10

Explanation: Let 

vector a = 5i + j – 3k

vector b = 3i – 4j + 7k

The scalar product of vectors a and b is given by

a.b = (5i + j – 3k).(3i – 4j + 7k)

⇒ a.b = (5 x 3) - (1 x 4) - (3 x 7)

⇒ a.b = 15 - 4 - 21 = -10

Ans. The correct answer is c. initial point, terminal point

Explanation: The point from which a vector starts is called its initial point, and the point where it ends is called its terminal point.

Ans. The correct answer is a. 1

Explanation: The given vector is

v = 1/√3 i + 1/√3 j + 1/√3 k

The magnitude of vector v is given by

|v| = (1/√3)² + (1/√3)² + (1/√3)²

⇒ |v| = (1/3) + (1/3) + (1/3)

⇒ |v| = 3/3 = 1

Ans. The correct answer is c. 45°

Explanation: Given

|A.B| = |A×B|

We have

|A.B| = AB cosθ and |A x B| = AB sinθ

⇒ AB cosθ = AB sinθ

⇒ sinθ/cosθ = 1

⇒ tanθ = 1

⇒ θ = 45°

Ans. The correct answer is a. Yes

Explanation: Yes, two different vectors can have the same magnitude.

The magnitude of vector 2i – j + 3k is equal to the magnitude of vector i + 3j – 2k.

Ans. The correct answer is b. 7

Explanation: Let the given vector be v = 6i + 2j + 3k

The magnitude of vector v is given by

|v| = √(6² + 2² + 3²) = 7

Ans. The correct answer is d. coinitial vectors

Explanation: Coinitial vectors are vectors that have the same initial points. It is not required that they be of the same magnitude and direction.

Ans. The correct answer is c. They have the same magnitude and direction

Explanation: If two vectors have the same magnitude and direction, they are said to be equal. They are coinitial if they have the same initial point and collinear if both vectors are parallel to the same line.

Ans. The correct answer is b. i + 2j

Explanation: The coordinates (1, 2, 0) can be represented in terms of position vector as (i + 2j).

Ans. The correct answer is d. 20

Explanation: We have

|a × b|² + |a.b|² = |a|² |b|²

⇒ 4² + 2² = |a|² |b|²

⇒ |a|² |b|² = 20

Ans. The correct answer is a. √34

Explanation: The given vector is v = -3i + 5j

The magnitude of vector v is given by

|v| = √(3² + 5²) = √34

Ans. The correct answer is a. Velocity

Explanation: Velocity is a vector quantity as it has both magnitude and direction. Time, weight, and volume all have magnitude but no direction. As a result, they are all scalar quantities.

Ans. The correct answer is b. 6 Newton

Explanation: 6 Newton is a vector quantity as it is a force. Force is a vector quantity that has both magnitude and direction.