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Class 12 Maths Practice Test - Product of Two Vectors
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Class 12 Maths Practice Test - Product of Two Vectors
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19 Questions

1. Find the angle between the vectors \(\vec{a}=-\hat{i}+\hat{j}-\hat{k}\) and \(\vec{b}=\hat{i}-\hat{j}\)
2. If two non-zero vectors \(\vec{a} \,and \, \vec{b}\) are perpendicular to each other then their scalar product is zero.
3. Find the scalar product of the vectors \(\vec{a}=2\hat{i}+5\hat{j}\) and \(\vec{b}=6\hat{i}-7\hat{j}\).
4. Find the angle between the vectors if \(|\vec{a}|=|\vec{b}|=3\sqrt{2}\) and \(\vec{a}.\vec{b}=9\sqrt{3}\).
5. Find the projection of vector \(\vec{b}=2\hat{i}+2\sqrt{2} \,\hat{j}-2\hat{k}\) on the vector \(\vec{a}=\hat{i}-\hat{j}-\sqrt{2} \,\hat{k}\).
6. Find the magnitude of \(\vec{a}\) and \(\vec{b}\) which are having the same magnitude and such that the angle between them is 60° and their scalar product is \(\frac{1}{4}\).
7. Find the angle between the two vectors \(\vec{a} \,and \, \vec{b}\) with magnitude 2 and \(\sqrt{3}\) respectively and \(\vec{a.} \, \vec{b}\)=4.
8. Find the angle between the two vectors \(\vec{a}\) and \(\vec{b}\) with magnitude \(\sqrt{3}\) and \(\sqrt{2}\) respectively and \(\vec{a.} \,\vec{b}=3\sqrt{2}\).
9. Find the vector product of the vectors \(\vec{a}=-\hat{j}+\hat{k}\) and \(\vec{b}=-\hat{i}-\hat{j}-\hat{k}\).
10. Find \(|\vec{a}+\vec{b}|\), if \(|\vec{a}|=3 \,and \,|\vec{b}|=4 \,and \,\vec{a}.\vec{b}=6\).
11. Find the angle between \(\vec{a} \,and \,\vec{b}\) if \(|\vec{a}|=2,|\vec{b}|=\frac{1}{2√3}\) and \(\vec{a}×\vec{b}=\frac{1}{2}\).
12. Find the scalar product of the vectors \(\vec{a}=6\hat{i}-7\hat{j}+5\hat{k} \,and \,\vec{b}=6\hat{i}-7\hat{k}\)
13. 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 \(|\vec{a}×\vec{b}|\).
14. Find the angle between the vectors \(\vec{a}=\hat{i}-\hat{j}+2\hat{k} \,and \,\vec{b}=3\hat{i}+2\hat{j}+4\hat{k}\).
15. If \(\vec{a} \,and \,\vec{b}\) are two non-zero vectors then \((\vec{a}-\vec{b})×(\vec{a}+\vec{b})\)=_________
16. Find the vector product of the vectors \(\vec{a}=2\hat{i}+4\hat{j}\) and \(\vec{b}=3\hat{i}-\hat{j}+2\hat{k}\).
17. Find the projection of vector \(\vec{a}=8\hat{i}-\hat{j}+6\hat{k}\) on vector \(\vec{b}= 4\hat{i}+3\hat{j}\).
18. 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.
19. Find the product \((\vec{a}+\vec{b}).(7\vec{a}-6\vec{b})\).

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