Physics - Vectors Question with Solution | TestHub

The resultant vector $\vec{R}$ is given by the sum of vectors $\vec{A}$ and $\vec{B}$.

$\vec{R}=\vec{A}+\vec{B}$

$\vec{R}=(-2\hat{i}+3\hat{j}+\hat{k})+(\hat{i}+2\hat{j}-4\hat{k})$

$\vec{R}=-\hat{i}+5\hat{j}-3\hat{k}$

The magnitude of the resultant vector is:

$|\vec{R}|=\sqrt{(-1{)}^2+(5{)}^2+(-3{)}^2}$

$|\vec{R}|=\sqrt{1+25+9}=\sqrt{35}$

The unit vector in the direction of the resultant vector is:

$\hat{R}=\frac{\vec{R}}{|\vec{R}|}=\frac{-\hat{i}+5\hat{j}-3\hat{k}}{\sqrt{35}}$

Answer: $\frac{-\hat{\mathrm{i}}+5\hat{\mathrm{j}}-3\hat{\mathrm{k}}}{\sqrt{35}}$