What is the projection of $\overrightarrow{a}=\left(2\hat{i}-\hat{j}+\hat{k}\right)$on$\overrightarrow{b}=\left(\hat{i}-2\hat{j}+\hat{k}\right)$ $?$

If $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|$, then

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two mutually perpendicular unit vectors then $(3\overrightarrow{a}+2\overrightarrow{b})·(5\overrightarrow{a}-6\overrightarrow{b})=$

If $\overrightarrow{a}=3\hat{i}+\hat{j}-2\hat{k}$ and $\overrightarrow{b}=\hat{i}+\lambda \hat{j}-3\hat{k}$ are perpendicular to each other then $\lambda =$

If $\theta$ is the angle between two unit vectors $\hat{a}$ and $\hat{b}$ then  $\frac{1}{2}|\hat{a}-\hat{b}|=?$

If $\overrightarrow{a}=\hat{i}-\hat{j}+2\hat{k}$ and $\overrightarrow{b}=2\hat{i}+3\hat{j}-4\hat{k}$ then $|\overrightarrow{a}\times \overrightarrow{b}|=?$

If $\overrightarrow{a}=\left(\hat{i}-2\hat{j}+3\hat{k}\right)$ and $\overrightarrow{b}=\left(\hat{i}-3\hat{k}\right)$ then $|\overrightarrow{b}\times 2\overrightarrow{a}|=$