$\vec{F} = 3 \hat{i} - 2 \hat{j} + 5 \hat{k}$

 এবং 

  $\vec{d} = 2 \hat{i} + \hat{j} - 3 \hat{k}$  

  $\left \lvert \vec{F} + 3 \vec{d} \right \rvert$ এর মান কত?

$\begin{aligned} |\mathbf{F}+3 \mathbf{d}| & =|3 \hat{\mathrm{i}}-2 \hat{\mathbf{j}}+5 \hat{\mathrm{k}}+6 \hat{\mathrm{i}}+3 \hat{\mathbf{j}}-9 \hat{\mathbf{k}}| \\ & =|9 \hat{\mathrm{i}}+\hat{\mathrm{j}}-4 \hat{\mathrm{k}}| \\ & =\sqrt{9^{2}+1^{2}+(-4)^{2}}=\sqrt{98} \end{aligned}$