Physics - Vectors Question with Solution | TestHub

Let $\vec{R}$ be the sum of the given vectors.

$\vec{R}=\vec{a}+\vec{b}+\vec{c}$

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

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

The magnitude of the sum vector is:

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

The unit vector along the direction of the sum is:

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

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