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:

If the position vector of one end of a line segment $AB$ is $2i + 3j - k$ and the position vector of its midpoint is $3(i + j + k)$,then what is the position vector of the other end?

In the figure,a vector $x$ satisfies the equation $x - w = v$. Then $x =$

If the vectors $\vec{a} = \lambda \hat{i} + 2\hat{j} - 3\hat{k}$ and $\vec{b} = \sqrt{\lambda} \hat{i} + \sqrt{13} \hat{j}$ have the same magnitude,then the value of $\lambda$ 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:

In a parallelogram $ABCD$,if $\vec{AC}$ and $\vec{BD}$ are the diagonals,then which of the following is equal to $\vec{AC} + \vec{BD}$?