Vector Components

Q.

Let $\stackrel{\rightharpoonup }{a}$, $\stackrel{\rightharpoonup }{b}$and $\stackrel{\rightharpoonup }{c}$ be a non-zero vectors such that $\left(\stackrel{\rightharpoonup }{a}\times \stackrel{\rightharpoonup }{b}\right)\times \stackrel{\rightharpoonup }{c}=-\frac{1}{4}\left|\stackrel{\rightharpoonup }{b}\right|\left|\stackrel{\rightharpoonup }{c}\right|\stackrel{\rightharpoonup }{a}$.If $\theta$is the acute angle between the vectors $\stackrel{\rightharpoonup }{b}$ and $\stackrel{\rightharpoonup }{c}$, then the angle between $\stackrel{\rightharpoonup }{a}$and $\stackrel{\rightharpoonup }{c}$ is?

1. $\frac{2\mathrm{\pi }}{3}$

2. $\frac{\mathrm{\pi }}{4}$

3. $\frac{\mathrm{\pi }}{3}$

4. $\frac{\mathrm{\pi }}{2}$

Q.

Which of these can most likely be $3\hat{i}+6\hat{j}$

1. 

2. 

3. 

4. 

Q.

Vectors $\overrightarrow{C}$ and $\overrightarrow{D}$ have magnitudes of 3 and 4 units respectively. What is the angle between the directions of $\overrightarrow{C}$ and $\overrightarrow{D}$ if the magnitude of vector product $\overrightarrow{C}\times \overrightarrow{D}$ is x and y respectively?

(x) 0 (y) 12 units

(i) 0 (ii)$\frac{\pi }{2}$ (iii)$\frac{\pi }{3}$ (iv) $\frac{\pi }{4}$

1. (x) - (iv); (y) - (iii)

2. (x) - (i); (y) - (ii)

3. (x) - (ii); (y) - (i)

4. (x) - (i); (y) - (iv)

Q. The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The triple product $\overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A})$ is equal to.

1. $A^{2}Bsi{n}^2\theta$
2. $A^{2}Bsin\theta cos\theta$
3. $A^{2}Bco{s}^2\theta$
4. \N

Q. A gun fires a bullet of mass $50\text{g}$ with a velocity of $30\text{m/s}$. Due to this, the gun is pushed back with a velocity of $1\text{m/s}$, then the mass of the gun is:

1. $1.5\text{kg}$
2. $5.5\text{kg}$
3. $0.5\text{kg}$
4. $3.5\text{kg}$