This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Types of Vectors”.

1. Two vectors having the same initial points are called as ________________

a) collinear vectors

b) unit vectors

c) coinitial vectors

d) equal vectors

View Answer

Explanation: The vectors which have the same initial points are called coinitial vectors. It is not necessary that they should have the same magnitude and direction.

2. A unit vector is a vector whose magnitude is unity.

a) True

b) False

View Answer

Explanation: The given statement is true. The vector whose magnitude is unity is called a unit vector. The unit vector in the given direction of given vector \(\vec{b}\) is denoted by \(\hat{b}\).

3. Which of the following vectors are collinear in the figure given below?

a) \(\vec{a}\), \(\vec{c}\) and \(\vec{d}\)

b) \(\vec{a}\), \(\vec{b}\) and \(\vec{d}\)

c) \(\vec{a}\) and \(\vec{d}\)

d) \(\vec{b}\) and \(\vec{d}\)

View Answer

Explanation: Collinear vectors are those vectors which are parallel to the same line irrespective of the magnitude and direction. In the given figure, \(\vec{a}\), \(\vec{b}\) and \(\vec{d}\) are collinear vectors.

4. In the figure given below, which vectors are coinitial but not equal?

a) \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\)

b) \(\vec{b}\) and \(\vec{c}\)

c) \(\vec{a}\) and \(\vec{b}\)

d) \(\vec{a}\) and \(\vec{c}\)

View Answer

Explanation: The vectors which start from the same initial point are called coinitial vectors. In the given figure, vectors \(\vec{a}\) and \(\vec{c}\) start from the same point but are of different magnitude. Therefore, vectors \(\vec{a}\) and \(\vec{c}\) ae coinitial but not equal.

5. Which of the following condition is true for equal vectors?

a) They have the same direction but not same magnitude

b) They have the same magnitude and direction

c) They have the same initial point

d) They are parallel to the same line

View Answer

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

6. The vector whose initial and final points coincide is called ____________

a) unit vector

b) coinitial vectors

c) equal vectors

d) zero vector

View Answer

Explanation: The vector whose initial and final points coincide is called zero vector or a null vector. It is denoted by \(\vec{0}\). It has zero magnitude and can be considered to have any direction.

7. The vectors which start from the same initial point are called collinear vectors.

a) True

b) False

View Answer

Explanation: The given statement is false. Collinear vectors are those vectors that are parallel same line irrespective of the direction and magnitude. The vectors which have the same initial point are called coinitial vectors.

8. In the given figure, which of the following vectors are coinitial?

a) \(\vec{a}\), \(\vec{c}\) and \(\vec{b}\)

b) \(\vec{d}\), \(\vec{c}\) and \(\vec{b}\)

c) \(\vec{a}\) and \(\vec{c}\)

d) \(\vec{b}\) and \(\vec{c}\)

View Answer

Explanation: Two vectors are said to coinitial if they have the same initial point. In the given figure, vectors \(\vec{a}\), \(\vec{c}\) and \(\vec{b}\) are starting from the point, hence they are coinitial.

9. Which of the following vectors are equal in the figure given below?

a) \(\vec{a}\) and c

b) \(\vec{c}\) and \(\vec{b}\)

c) \(\vec{a}\) and \(\vec{b}\)

d) \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\)

View Answer

Explanation: Two vectors are said to be equal, if they have the same magnitude. In the given figure, vectors \(\vec{a}\) and \(\vec{b}\) have the same magnitude. Hence, they are equal.

10. Which of the following is the condition for two vectors to be Collinear?

a) The vectors should be parallel to the same line

b) The vectors should have the same initial point

c) The vectors should have the same magnitude

d) The vectors should have the magnitude 1 and 0 respectively

View Answer

Explanation: If two or more vectors are parallel to the same line then they are called collinear vectors. It is not necessary that they should have the same magnitude and direction.

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