This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Vector Algebra Basics”.

1. Which of the following holds true for a vector quantity?

a) It has only magnitude

b) It has only direction

c) A vector has both direction and magnitude

d) A vector can never be negative

View Answer

Explanation: A quantity which has both magnitude and direction is called a

**vector**quantity. The quantity which has only magnitude but no direction is called a

**scalar**quantity.

2. A scalar quantity has only magnitude and no direction.

a) True

b) False

View Answer

Explanation: The given statement is true. The quantity which has only magnitude and no direction is called scalar quantity.

Example: Time. Time is a scalar quantity which has only magnitude and no direction.

3. Which of the following id the correct symbol for denoting a given vector A?

a) |A|

b) [A]

c) \(\vec{A}\)

d) \(\underset{A}{\rightharpoonup }\)

View Answer

Explanation: The correct way denoting a vector given vector A is \(\vec{A}\).

4. Which of the following is used to represent the magnitude of vector \(\vec{A}\)?

a) \(\hat{A}\)

b) |\(\vec{A}\)|

c) \(\underset{A}{\leftrightarrow}\)

d) \(\vec{A}\)

View Answer

Explanation: The correct way of representing the magnitude of a given vector A is|\(\vec{A}\)|. The magnitude of a vector is the distance between the initial and the terminal points of a vector.

5. For a given vector A, |\(\vec{A}\)| can be less than zero.

a) True

b) False

View Answer

Explanation: The given statement is false.|\(\vec{A}\)| denotes the magnitude of the vector and since length of the line of the line can never be negative,|\(\vec{A}\)|<0 has no meaning.

6. Which of the given qualities is a vector?

a) Speed

b) Time

c) Weight

d) Volume

View Answer

Explanation: Speed is a vector quantity as it has both magnitude and direction. Time, weight, volume have only magnitude and no direction. Hence, they all are scalar quantity.

7. Which of the following is not a vector quantity?

a) Speed

b) Density

c) Force

d) Velocity

View Answer

Explanation: Density is a scalar quantity as it has only magnitude but no direction. Speed, force, velocity has both magnitude and direction. Therefore, they all are vectors.

8. Which of the below given is a vector quantity?

a) 8 kg

b) 4 seconds

c) 6 Newton

d) 90 cm^{3}

View Answer

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

9. Which of the following is a scalar quantity?

a) 80m^{3}

b) 5 Newton

c) 7 m/s towards east

d) 55m/s^{2}

View Answer

Explanation: 80 cm

^{3}is a scalar quantity as it is denoting volume. Volume is a scalar quantity and has only magnitude but no direction.

10. If l, m, n are the direction cosines of a position vector \(\vec{a}\), then which of the following is true?

a) l^{2}+m^{2}-n^{2}=0

b) lmn=1

c) l^{2}+m^{2}+n^{2}=1

d) l^{2} m^{2}+n^{2}=1

View Answer

Explanation: Consider \(\vec{a}\) is the position vector of a point M(x,y,z) and α, β, γ are the angles, made by the vector \(\vec{a}\) with the positive directions of x, y and z respectively. The cosines of the angles, cosα, cosβ, cosγ are the direction cosines of the vector \(\vec{a}\) denoted by l, m, n, then

cos

^{2}α+cos

^{2}β+cos

^{2}γ=1 i.e.l

^{2}+m

^{2}+n

^{2}=1.

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