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

Vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other when $3 a+2 b=7$, the ratio of a to $b$ is $\frac{x}{2}$. The value of $x$ is $..............$

Which of the following is the unit vector perpendicular to $\overrightarrow A $ and $\overrightarrow B $

Two vectors $\overrightarrow A $ and $\overrightarrow B $ are at right angles to each other, when

A particle moves in the $x-y$ plane under the action of a force $\overrightarrow F $ such that the value of its linear momentum $(\overrightarrow P )$ at anytime t is ${P_x} = 2\cos t,\,{p_y} = 2\sin t.$ The angle $\theta $between $\overrightarrow F $ and $\overrightarrow P $ at a given time $t$. will be $\theta =$ ........... $^o$

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