Question

The length of the projection of the lines segment joining the points $x+y+z=7$ is:

• A. $\frac{2}{\sqrt{3}}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\sqrt{\frac{2}{3}}$

Answer 1

The correct option is D $\sqrt{\frac{2}{3}}$

$HerePQistheprojectionAlsoPQ=BCAC=\widehat{AB}.\widehat{BC}=\left(i+\hat{k}\right).\left(\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\right)=\frac{2}{\sqrt{3}}$

$Also,AB=\sqrt{2}AB=A{C}^2+B{C}^2$

$2=\frac{4}{3}+B{C}^{2}B{C}^2=\frac{2}{3}BC=\sqrt{\frac{2}{3}}$

Hence,

$\therefore$ Option $D$ is correct answer.