If $a = 4 \hat{i} + 6 \hat{j}$,$b = 3 \hat{j} + 4 \hat{k}$,and $c$ is the projection vector of $a$ on $b$,then $c$ and $|c|$ respectively are

If $\vec{a} = -4 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and $\vec{b} = \sqrt{2} \hat{i} - \sqrt{2} \hat{j}$ are two vectors,then the angle between the vectors $2 \vec{a}$ and $\frac{\vec{b}}{2}$ is (in $^{\circ}$)

If the position vectors of $A, B$ and $C$ are respectively $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $3 \hat{i}-4 \hat{j}-4 \hat{k}$,then $\cos ^2 A$ is equal to

Let $\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}$,$\vec{b}=4 \hat{i}+\hat{j}+7 \hat{k}$,and $\vec{c}=\hat{i}-3 \hat{j}+4 \hat{k}$ be three vectors. If a vector $\vec{p}$ satisfies $\vec{p} \times \vec{b}=\vec{c} \times \vec{b}$ and $\vec{p} \cdot \vec{a}=0$,then $\vec{p} \cdot(\hat{i}-\hat{j}-\hat{k})$ is equal to

If $a$ and $b$ are unlike vectors,then $a \cdot b =$

Scalar projection of the line segment joining the points $A(-2,0,3)$ and $B(1,4,2)$ on the line whose direction ratios are $6,-2,3$ is