Question

If $\overline{A}=\hat{i}-2\hat{j}+3\hat{k},\overline{B}=4\hat{i}+4\hat{j}-4\hat{k}$ and $\overrightarrow{C}=5\hat{i}-8\hat{j}+9\hat{k}$ then $|\overline{A}+\overline{B}+\overline{C}|$ is?

• A. $\sqrt{114}$
• B. $\sqrt{105}$
• C. $10\sqrt{2}$
• D. $16$

Answer 1

The correct option is C $10\sqrt{2}$

$\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=[\hat{i}-2\hat{j}+3\hat{k}]$+$[4\hat{i}+4\hat{j}-4\hat{k}]$+$[5\hat{i}-8\hat{j}+9\hat{k}]$

$=10\hat{i}-6\hat{j}+8\hat{k}$

$|\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}|=\sqrt{{10}^2+{(-6)}^2+{\left(8\right)}^2}=10\sqrt{2}$