What should be added to the vector $a = 3i + 4j - 2k$ to obtain the resultant vector $i$?

The position vector of a point lying on the line joining the points whose position vectors are $\hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is:

The magnitudes of mutually perpendicular forces $a, b$ and $c$ are $2, 10$ and $11$ respectively. Then the magnitude of its resultant is

If $M_1, M_2, M_3$ and $M_4$ are respectively the magnitudes of the vectors $\vec{a}_1 = 2\hat{i} - \hat{j} + \hat{k}$,$\vec{a}_2 = -3\hat{i} - 4\hat{j} - 4\hat{k}$,$\vec{a}_3 = -\hat{i} + \hat{j} - \hat{k}$,and $\vec{a}_4 = -\hat{i} + 3\hat{j} + \hat{k}$,then the correct order of $M_1, M_2, M_3$ and $M_4$ is:

If $a = (1, -1)$ and $b = (-2, m)$ are two collinear vectors,then $m = $

If the position vectors of $A, B, C,$ and $D$ are $2i + j,$ $i - 3j,$ $3i + 2j,$ and $i + \lambda j$ respectively and $\overrightarrow{AB} \parallel \overrightarrow{CD},$ then the value of $\lambda$ is: