Angle between Two Vectors

Q.

Can you cross product a scalar and a vector?

Q.

$\overrightarrow{a}$ and $\overrightarrow{c}$ are unit vectors and $|\overrightarrow{b}|=4.$ The angle between $\overrightarrow{a}and\overrightarrow{c}isco{s}^{-1}\left(\frac{1}{4}\right).$
If $\overrightarrow{b}-2\overrightarrow{c}=\lambda \overrightarrow{a}$, then $\lambda$ is

1. $3or-4$

2. $\frac{1}{4}or\frac{3}{4}$

3. $-3or4$

4. $-\frac{1}{4}or\frac{3}{4}$

Q. If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors inclined at an angle $\theta$ such that $\overrightarrow{a}+\overrightarrow{b}$ is a unit vector, then $\theta$ is equal to

1. $\frac{\pi }{3}$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{2}$
4. $\frac{2\pi }{3}$

Q. If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors such that $\overrightarrow{a}.\overrightarrow{b}=0$ and $\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{0}$, then

1. $\overrightarrow{a}||\overrightarrow{b}$
2. $\overrightarrow{a}\perp \overrightarrow{b}$
3. $eitherparallelorperpedicular$
4. $Noneoftheabove$

Q. What is the angle between the two vectors shown in the figure?

1. $\theta$
2. $\frac{\theta }{2}$
3. $\pi -\theta$
4. $\theta -\pi$