If $\vec A = 2\hat i + \hat j - \hat k,\,\vec B = \hat i + 2\hat j + 3\hat k$ and $\vec C = 6\hat i - 2j - 6\hat k$ then the angle between $(\vec A + \vec B)$ and $\vec C$ wil be ....... $^o$

Define the scalar product and obtain the magnitude of a vector from it. Mention the direction of scalar product.

If $\vec{a}$ and $\vec{b}$ makes an angle $\cos ^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ The integer value of $n$ is . . . . . . .. 

Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$. What is the area of parallelogram

The angle between two vectors $4\hat i + 3\hat j + \hat k$ and $-3\hat i + 2\hat j + 6\hat k$ is ....... $^o$

A vector $\overrightarrow{ A }$ points vertically upward and $\overrightarrow{ B }$ points towards north. The vector product $\overrightarrow{ A } \times \overrightarrow{ B }$ is