If the points $a + b$,$a - b$,and $a + kb$ are collinear,then $k =$

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

If vectors $\overrightarrow{a}_{1} = x \hat{i} - \hat{j} + \hat{k}$ and $\overrightarrow{a}_{2} = \hat{i} + y \hat{j} + z \hat{k}$ are collinear,then a possible unit vector parallel to the vector $x \hat{i} + y \hat{j} + z \hat{k}$ is ...... .

$\hat{i}-2 \hat{j}+\hat{k}$, $2 \hat{i}+\hat{j}-\hat{k}$, and $\hat{i}-\hat{j}-2 \hat{k}$ are the position vectors of the vertices $A, B$, and $C$ of a triangle $ABC$ respectively. If $D$ and $E$ are the midpoints of $BC$ and $CA$ respectively, then the unit vector along $\overrightarrow{DE}$ is

Three points whose position vectors are $a + b$,$a - b$,and $a + kb$ will be collinear if the value of $k$ is:

In the given figure,which of the vectors are equal?