Question

$\overline{a},\overline{b},\overline{c}$ are three vectors that $\left|\overline{a}\right|=1,\left|\overline{b}\right|=2,\left|\overline{c}\right|=3$ and $\overline{b},\overline{c}$ are perpendicular. If projection of $\overline{b}$ on $\overline{c}$ is the same as the projection of on $\overline{a}$, then $|\overline{a}-\overline{b}+\overline{c}|=$

• A. $\sqrt{2}$
• B. $\sqrt{7}$
• C. $\sqrt{14}$
• D. $\sqrt{21}$

Answer 1

The correct option is C $\sqrt{14}$

Given, $|\overline{a}|=1,|\overline{b}=2,|\overline{c}=3||$

$\frac{\overline{b}.\overline{a}}{\left|\overline{a}\right|}=\frac{\overline{c}.\overline{a}}{\left|\overline{a}\right|}$
${|\overline{a}+\overline{b}|}^2={\left|\overline{a}\right|}^2-{\left|\overline{b}\right|}^2+{\left|\overline{c}\right|}^2-2\overline{a}.\overline{b}-2\overline{b}.\overline{c}+2\overline{c}.\overline{a}=14$

Therefore, $|\overline{a}-\overline{b}+\overline{c}|=\sqrt{14}$.