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
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Answer: a
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(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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Answer: d
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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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Answer: d
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4. If \(|\vec{a}|\) = 4 and -3 ≤ λ ≤ 2 then the range of \(|\lambda \vec{a}|\) is Answer: c
(a) [0, 8] (b) [-12, 8] (c) [0, 12] (d) [8, 12] Answer/Explanation
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5.
(a) 30°
(b) 45°
(c) 60°
(d) 90°
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Answer: a
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6.
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Answer: c
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7.
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Answer: b
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8.
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Answer: a
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9. Mathematically a vector is defined as a “directed line segment.” State true or false.
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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] Answer: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:Answer/Explanation
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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] Answer:Answer/Explanation
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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] Answer: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:Answer/Explanation
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51. Write a unit vector perpendicular to both the Answer:
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52.
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Explaination: coplanr
53.
(a) 4
(b) 0
(c) -3
(d) 2
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Answer: b
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54.
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55.
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