CBSE Class 12 Maths Vector Algebra Quiz 4

1. If \(\vec{a}\) and \(\vec{b}\) are any two vector then (\(\vec{a}\) × \(\vec{b}\))² is equal to

A (\(\vec{a}\))²(\(\vec{b}\))² – (\(\vec{a}\).\(\vec{b}\))² B (\(\vec{a}\))² (\(\vec{b}\))² + (\(\vec{a}\).\(\vec{b}\))² C (\(\vec{a}\).\(\vec{b}\))² D (\(\vec{a}\))²(\(\vec{b}\))²

2. If \(\hat{a}\) and \(\hat{b}\) be two unit vectors and 0 is the angle between them, then |\(\hat{a}\) – \(\hat{b}\)| is equal to

A sin \(\frac{θ}{2}\) B 2 sin \(\frac{θ}{2}\) C cos \(\frac{θ}{2}\) D 2 cos \(\frac{θ}{2}\)

3. The angle between the vector 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) – \(\hat{k}\) is

A \(\frac{π}{2}\) B \(\frac{π}{4}\) C \(\frac{π}{3}\) D 0

4. If \(\vec{a}\) = \(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\), \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) – \(\hat{k}\), \(\vec{c}\) = 3\(\hat{i}\) – p\(\hat{j}\) – 5\(\hat{k}\) are coplanar then P =

A 6 B -6 C 2 D -2

5. The distance of the point (- 3, 4, 5) from the origin

A 50 B 5√2 C 6 D None of these

6. If \(\vec{AB}\) = 2\(\hat{i}\) + \(\hat{j}\) – 3\(\hat{k}\) and the co-ordinates of A are (1, 2, -1) then coordinate of B are

A (2, 2, -3) B (3, 2, -4) C (4, 2, -1) D (3, 3, -4)

7. If \(\vec{b}\) is a unit vector in xy-plane making an angle of \(\frac{π}{4}\) with x-axis. then \(\vec{b}\) is equal to

A \(\hat{i}\) + \(\hat{j}\) B \(\vec{i}\) – \(\vec{j}\) C \(\frac{\vec{i}+\vec{j}}{√2}\) D \(\frac{\vec{i}-\vec{j}}{√2}\)

8. \(\vec{a}\) = 2\(\hat{i}\) + \(\hat{j}\) – 8\(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) then the magnitude of \(\vec{a}\) + \(\vec{b}\) is equal to

A 13 B \(\frac{13}{4}\) C \(\frac{3}{13}\) D \(\frac{4}{13}\)

9. The vector in the direction of the vector \(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\) that has magnitude 9 is

A \(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\) B \(\frac{\hat{i}-2\hat{j}+2\hat{k}}{3}\) C 3(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\)) D 9(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))

10. The position vector of the point which divides the join of points 2\(\vec{a}\) – 3\(\vec{b}\) and \(\vec{a}\) + \(\vec{b}\) in the ratio 3 : 1 is

A \(\frac{3\vec{a}-2\vec{b}}{2}\) B \(\frac{7\vec{a}-8\vec{b}}{2}\) C \(\frac{3\vec{a}}{2}\) D \(\frac{5\vec{a}}{4}\)