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

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 10 Vector Algebra. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Vector Algebra MCQs Pdf with Answers to know their preparation level.

## Vector Algebra Class 12 Maths MCQs Pdf

1. A vector equally inclined to axes is

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

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

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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]

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5.

(a) 30°
(b) 45°
(c) 60°
(d) 90°

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6.

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7.

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8.

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

Explaination: True

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

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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 _________ .

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

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

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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?

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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]

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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]

Explaination:
For vectors to be collinear $$\frac{2}{a}=\frac{-3}{6}=\frac{4}{-8}$$
⇒ a = -4

20. ABCDEF is a regular hexagon,

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

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

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

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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 __________ .

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

State true or false.

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27.
are perpendicular. State true or false.

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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]

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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]

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51. Write a unit vector perpendicular to both the
[AI 2015]

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52.

Explaination: coplanr

53.

(a) 4
(b) 0
(c) -3
(d) 2

Explaination:

54.