If $a = 4i + 6j$ and $b = 3j + 4k$,what is the vector component of $a$ along the direction of $b$?

Let $\overline{u}, \overline{v}$ and $\overline{w}$ be the vectors such that $|\overline{u}|=1, |\overline{v}|=2, |\overline{w}|=3$. If the projection of $\overline{v}$ along $\overline{u}$ is equal to that of $\overline{w}$ along $\overline{u}$ and $\overline{v}, \overline{w}$ are perpendicular to each other,then $|\overline{u}-\overline{v}+\overline{w}|$ is equal to

Let $\vec{a} = 5\hat{i} - \hat{j} - 3\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + 5\hat{k}$ be two vectors. Then which one of the following statements is $TRUE$?

If $\vec{b}=2 \hat{i}-\hat{j}-\hat{k}$, $\vec{a}=3 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\vec{b} \times(\vec{a} \times \vec{b})=\frac{\vec{a}-k \vec{b}}{l}$, then $\frac{k}{l|\vec{b}|}$ is

The component of $\hat{i}$ in the direction of the vector $\hat{i}+\hat{j}+2 \hat{k}$ is

$A$ particle acted on by two forces $3i + 2j - 3k$ and $2i + 4j + 2k$ is displaced from the point $i + 2j + k$ to $5i + 4j + 2k.$ The total work done by the forces is equal to ............ $unit$.