If $a = i - 2j$ and $b = 2i + \lambda j$ are parallel,then $\lambda$ is

$a$ and $b$ are non-collinear vectors. If $c=(x-2)a+b$ and $d=(2x+1)a-b$ are collinear vectors,then the value of $x = \ldots$

The position vectors of $P$ and $Q$ are $5i + 4j + ak$ and $-i + 2j - 2k$ respectively. If the distance between them is $7$,then the value of $a$ will be:

If $\hat{i}, \hat{j}, \hat{k}$ are unit vectors,then which of the following is true?

If $D, E$ and $F$ are respectively the mid-points of $AB, AC$ and $BC$ in $\triangle ABC$, then $\overrightarrow{BE} + \overrightarrow{AF}$ is equal to :

The vector having magnitude of $2 \sqrt{29}$ units in the direction of vector $\vec{a} = 4 \hat{i} + 3 \hat{j} - 2 \hat{k}$ is . . . . . . .