# Maths MCQs for Class 12 with Answers Chapter 10 Vector Algebra

## Vector Algebra Class 12 Maths MCQs Pdf

1. A vector equally inclined to axes is

**Answer/Explanation**

Answer: a

Explaination:

(a), as direction ratios are 1, 1, 1 and

direction cosines \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)

⇒ cos α = cos β = cos γ

⇒ α = β = γ

2. The position vector of a point which divides the join of points with position vectors \(\vec{a}+\vec{b}\) and \(2 \vec{a}-\vec{b}\) in the ratio 1:2 internally is

**Answer/Explanation**

Answer: d

Explaination:

3. A vector in the direction of vector \(\hat{i}-2 \hat{j}+2 \hat{k}\) that has magnitude 15 is

**Answer/Explanation**

Answer: d

Explaination:

4. If \(|\vec{a}|\) = 4 and -3 ≤ λ ≤ 2 then the range of \(|\lambda \vec{a}|\) is

(a) [0, 8] (b) [-12, 8] (c) [0, 12] (d) [8, 12]

**Answer/Explanation**

Answer: c

Explaination:

5.

(a) 30°

(b) 45°

(c) 60°

(d) 90°

**Answer/Explanation**

Answer: a

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6.

**Answer/Explanation**

Answer: c

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7.

**Answer/Explanation**

Answer: b

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8.

**Answer/Explanation**

Answer: a

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9. Mathematically a vector is defined as a “directed line segment.” State true or false.

**Answer/Explanation**

Answer:

Explaination: True

10. If vectors are equal then their magnitudes are equal but the converse may not be true. State true or false.

**Answer/Explanation**

Answer:

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11. Given vector \(\overrightarrow{P Q}=2 \hat{i}+\hat{j}-3 \hat{k}\) and position vector of point P is \(3 \hat{j}-2 \hat{k}\), then position vector of point Q is _________ .

**Answer/Explanation**

Answer:

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12. Find a unit vector in the direction of \(\overrightarrow{a}=3 \hat{i}-2 \hat{j}+6 \hat{k}\)

**Answer/Explanation**

Answer:

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13. For what value of p, is (\(\hat{i}+ \hat{j}- \hat{k}\))p a irnit vector?

**Answer/Explanation**

Answer:

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14. If \(\overrightarrow{A B}=2 \hat{i}+\hat{j}-2 \hat{k}\) and \(\overrightarrow{B C}=6 \hat{i}+3\hat{j}-6 \hat{k}\), can we say that the points A, B, C are collinear?

**Answer/Explanation**

Answer:

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15. In the given figure, find

(i) parallel or collinear vectors

(ii) co-initial vectors

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16.

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17.

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18. Find a vector in the direction of \(\vec{a}=\vec{i}-2 \hat{j}\) whose magnitude is 7. [NCERT]

**Answer/Explanation**

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19. For what value of ‘a’ the vectors \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(\hat{a} \hat{i}+\hat{6} \hat{j}-8 \hat{k}\) are collinear?[Delhi2011]

**Answer/Explanation**

Answer:

Explaination:

For vectors to be collinear \(\frac{2}{a}=\frac{-3}{6}=\frac{4}{-8}\)

⇒ a = -4

20. ABCDEF is a regular hexagon,

**Answer/Explanation**

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21. The position vectors A, B, C, D are

**Answer/Explanation**

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22. Write the direction cosines of the vector \(-2 \hat{i}+\hat{j}-5 \hat{k}\) [Delhi 2011]

**Answer/Explanation**

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23. Show that the vector \( \hat{i}+\hat{j}+ \hat{k}\) is equally inclined to axes.

**Answer/Explanation**

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24. Write a unit vector in the direction of the

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25. The value of X for which vectors

are orthogonal is __________ .

**Answer/Explanation**

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26. For any non zero vector \(\vec{a}\),

State true or false.

**Answer/Explanation**

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27.

are perpendicular. State true or false.

**Answer/Explanation**

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28. Find the angle between the vectors

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29.

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30.

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31. If \(\vec{p}\) is a unit vector and

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32.

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33.

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34.

\(\vec{b}\) are along adjacent sides of a rectangle.

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35.

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36. Find the magnitude of each of the two vectors \(\vec{a}\) and \(\vec{b}\), having the same magnitude such that the angle between them is 60° and their scalar product is \(\frac{9}{2}\). [CBSE 2018]

**Answer/Explanation**

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37.

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38.

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39.

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40.

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41.

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42.

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43.

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44.

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45.

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46.

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47.

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48.

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49.

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50. Write the value of \((\hat{i} \times \hat{j}) . \hat{k}+\hat{i} \hat{j}\) [AI 2012]

**Answer/Explanation**

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51. Write a unit vector perpendicular to both the

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52.

**Answer/Explanation**

Answer:

Explaination: coplanr

53.

(a) 4

(b) 0

(c) -3

(d) 2

**Answer/Explanation**

Answer: b

Explaination:

54.

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55.

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