Question

The length of the projection of the line segement joining the points $(5,-1,4)$ and $(4,-1,3)$ on the plane, $x+y+z=7$ is

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

Answer 1

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

$\begin{array}{c}1,0,1\to dr,sofline\\ \cos \theta =\frac{1+0+1}{\sqrt{2}\sqrt{3}}=\sqrt{\frac{2}{3}}\\ Ab=\sqrt{1+1}=\sqrt{2}\\ pojection=AB=\sqrt{2}\sqrt{1-\frac{2}{3}}\\ =\sqrt{2}\sqrt{\frac{1}{3}}\\ =\sqrt{\frac{2}{3}}\end{array}$