The maximum and minimum magnitude of the resultant of two given vectors are $17$ units and $7$ units respectively. If these two vectors are at right angles to each other,the magnitude of their resultant is

$A$ man travels $30 \ m$ along the direction of $3 \hat{i} + 4 \hat{j}$ and then moves '$d$' meters perpendicular to the initial direction such that his total displacement is along the $x$-axis. What is the value of '$d$' in meters?

Two particles are located at an equal distance from the origin. The position vectors of these are represented by $\overrightarrow{A} = 2\hat{i} + 3n\hat{j} + 2\hat{k}$ and $\overrightarrow{B} = 2\hat{i} - 2\hat{j} + 4p\hat{k}$,respectively. If both vectors are at a right angle to each other,the value of $n^{-1}$ is . . . . . . .

If $\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ and $\overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$,then the scalar and vector products of $\overrightarrow{ F }$ and $\overrightarrow{ r }$ have the magnitudes respectively as

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Resultant of two mutually perpendicular vectors	$(a)$ Along the bisector of the angle between them
$(2)$ Direction of $\overrightarrow A \times \overrightarrow B$	$(b)$ Coplanar
	$(c)$ Perpendicular to the plane containing $\overrightarrow A$ and $\overrightarrow B$

Which of the following is not true? Given $\overrightarrow A = 3\hat i + 4\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,where $A$ and $B$ are the magnitudes of $\overrightarrow A$ and $\overrightarrow B$.