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Class 12 Mathematics: Vector Algebra
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MCQs on vector algebra basics, vectors types, vectors addition, vector multiplication by scalar and two vectors product.

Class 12 Mathematics: Vector Algebra
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25 Questions

1. If l, m, n are the direction cosines of a position vector \(\vec{a}\), then which of the following is true?
2. Find the angle between the vectors \(\vec{a}=\hat{i}-\hat{j}+2\hat{k} \,and \,\vec{b}=3\hat{i}+2\hat{j}+4\hat{k}\).
3. Which of the following condition is true for equal vectors?
4. If \(\vec{a}\)=\(\hat{i}\)+4\(\hat{j}\) and \(\vec{b}\)=3\(\hat{i}\)-3\(\hat{j}\). Find the magnitude of \(\vec{a}+\vec{b}\).
5. Find the sum of the vectors \(\vec{a}\)=8\(\hat{i}\)+5\(\hat{j}\) and \(\vec{b}\)=-2\(\hat{i}\)+6\(\hat{j}\)
6. Find the sum of the vectors \(\vec{a}\)=6\(\hat{i}\)-3\(\hat{j}\) and \(\vec{b}\)=5\(\hat{i}\)+4\(\hat{j}\).
7. A unit vector is a vector whose magnitude is unity.
8. In the given figure, which of the following vectors are coinitial?
mathematics-questions-answers-types-vectors-q8
9. Direction of λ\(\vec{a}\) and \(\vec{a}\) is same if λ is _______
10. Find the projection of vector \(\vec{a}=8\hat{i}-\hat{j}+6\hat{k}\) on vector \(\vec{b}= 4\hat{i}+3\hat{j}\).
11. What is direction of vector \(\vec{a}\) if it is multiplied with -λ?
12. Find the vector product of the vectors \(\vec{a}=-\hat{j}+\hat{k}\) and \(\vec{b}=-\hat{i}-\hat{j}-\hat{k}\).
13. If \(\vec{a}=\hat{i}-\hat{j}+3\hat{k}, \,\vec{b}=5\hat{i}-2\hat{j}+\hat{k} \,and \,\vec{c}=\hat{i}-\hat{j}\) are such that \(\vec{a}+μ\vec{b}\) is perpendicular to \(\vec{c}\), then the value of μ.
14. Evaluate the product \((2\vec{a}+5\vec{b}).(4\vec{a}-5\vec{b})\).
15. The vectors which start from the same initial point are called collinear vectors.
16. Find vector \(\vec{b}\), if \(\vec{a}+\vec{b}\)+\(\vec{c}\)=8\(\hat{i}\)+2\(\hat{j}\) where \(\vec{a}\)=\(\hat{i}\)-6\(\hat{j}\) and \(\vec{c}\)=3\(\hat{i}\)+7\(\hat{j}\).
17. If \(\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}\) and \(\vec{b}=4\hat{i}-2\hat{j}+3\hat{k}\). Find \(|\vec{a}×\vec{b}|\).
18. Which of the following is the condition for two vectors to be Collinear?
19. If \(\vec{a}\)=9\(\hat{i}\)-2\(\hat{j}\)+7\(\hat{k}\), \(\vec{b}\)=5\(\hat{i}\)+\(\hat{j}\)-3\(\hat{k}\), find \(\vec{a}+\vec{b}\).
20. If k is any scalar and \(\vec{a}\), \(\vec{b}\) be vectors then k (\(\vec{a}\)+ \(\vec{b}\))= ________
21. Find the magnitude of \(\vec{a}+\vec{b}\), if \(\vec{a}\)=4\(\hat{i}\)+9\(\hat{j}\) and \(\vec{b}\)=6\(\hat{i}\).
22. If \(\vec{a}\)=3\(\hat{i}\)+2\(\hat{j}\)+2\(\hat{k}\), \(\vec{b}\)=2\(\hat{i}\)-8\(\hat{j}\)+\(\hat{k}\), find \(\vec{a}+\vec{b}\).
23. Find the angle between the two vectors \(\vec{a}\) and \(\vec{b}\) with magnitude \(\sqrt{3}\) and \(\sqrt{2}\) respectively and \(\vec{a.} \,\vec{b}=3\sqrt{2}\).
24. Find vector \(\vec{c}\), if \(\vec{a}\)–\(\vec{b}\)+\(\vec{c}\)=6\(\hat{i}\)+8\(\hat{j}\) where \(\vec{a}\)=7\(\hat{i}\)+2\(\hat{j}\) and \(\vec{b}\)=4\(\hat{i}\)-5\(\hat{j}\).
25. Find the product \((\vec{a}+\vec{b}).(7\vec{a}-6\vec{b})\).

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