MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers

 

Vector Algebra Class 12 Maths MCQs Pdf

1. A vector equally inclined to axes is

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Answer: a
Explaination:
(a), as direction ratios are 1, 1, 1 and
direction cosines 13√,13√,13√
⇒ cos α = cos β = cos γ
⇒ α = β = γ

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2. The position vector of a point which divides the join of points with position vectors a⃗ +b⃗  and 2a⃗ −b⃗  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 i^−2j^+2k^ that has magnitude 15 is

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Answer: d
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4. If |a⃗ | = 4 and -3 ≤ λ ≤ 2 then the range of |λa⃗ | is
(a) [0, 8]
(b) [-12, 8]
(c) [0, 12]
(d) [8, 12]

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Answer: c
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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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Answer:
Explaination: True

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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 PQ−→−=2i^+j^−3k^ and position vector of point P is 3j^−2k^, then position vector of point Q is _________ .

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12. Find a unit vector in the direction of a→=3i^−2j^+6k^

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13. For what value of p, is (i^+j^−k^)p a irnit vector?

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14. If AB−→−=2i^+j^−2k^ and BC−→−=6i^+3j^−6k^, 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 a⃗ =i⃗ −2j^ whose magnitude is 7. [NCERT]

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19. For what value of ‘a’ the vectors 2i^−3j^+4k^ and a^i^+6^j^−8k^ are collinear?[Delhi2011]

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Answer:
Explaination:
For vectors to be collinear 2a=−36=4−8
⇒ a = -4

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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 −2i^+j^−5k^ [Delhi 2011]

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23. Show that the vector i^+j^+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 a⃗ ,

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 p⃗  is a unit vector and

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32.

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33.

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34. 
b⃗  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 a⃗  and b⃗ , having the same magnitude such that the angle between them is 60° and their scalar product is 92. [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 (i^×j^).k^+i^j^ [AI 2012]

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

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52.

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Explaination: coplanr

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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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