The angle made by the vector $\overrightarrow{A}=\hat{i}+\hat{j}$ with $x-$axis is-

Q. The angle made by the vector $\overrightarrow{A}=\hat{i}+\hat{j}$ with $x-$axis is

Q. Given two vectors $\overrightarrow{A}=\hat{i}-2\hat{j}-3\hat{k}$ and $\overrightarrow{B}=4\hat{i}-2\hat{j}+6\hat{k}$, the angle made by $(\overrightarrow{A}+\overrightarrow{B})$ with x-axis is:

Q. Find a unit vector $\overrightarrow{a}$ which makes an angle $\left(\pi /4\right)$ with axis of z & is such that $\overrightarrow{a}+\hat{i}+\hat{j}$ is a unit vector

Q. A non-zero vector $\overrightarrow{a}$ is parallel to the line of intersection of the plane determined by the vectors $\hat{i},\hat{i}+\hat{j}$ and the plane determined by the vectors $\hat{i}-\hat{j},\hat{j}+\hat{k}$. The angle between $\overrightarrow{a}$ and the vector $\hat{i}-2\hat{j}+2\hat{k}$ is