$A$ person moves $30 \,m$ North and then $20 \,m$ towards East and finally $30 \sqrt{2} \,m$ in South-West direction. The displacement of the person from the origin will be

If $\overrightarrow{R}$ is the resultant vector of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$,then $|\overrightarrow{R}|$ is . . . . . . $|\overrightarrow{A}| + |\overrightarrow{B}|$.

$A$ car travels $6 \, km$ at an angle of $45^\circ$ north of east and then travels $4 \, km$ at an angle of $135^\circ$ north of east. How far is the final point from the starting point? What angle does the straight line joining its initial and final position make with the east?

If $\overrightarrow A = 2\widehat i + 3\widehat j + 4\widehat k$ and $\overrightarrow B = \widehat i - \widehat j + \widehat k$,find their subtraction $\overrightarrow A - \overrightarrow B$ using the algebraic method.

The three vectors $\vec A = 3\hat i - 2\hat j + \hat k$,$\vec B = \hat i - 3\hat j + 5\hat k$,and $\vec C = 2\hat i + \hat j - 4\hat k$ form:

Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes $3 \text{ units}$ and $4 \text{ units}$ respectively. If the angle between them is $60^{\circ}$,find the magnitude of their resultant vector.