Question

The length of the projection of the line segment 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

Answer: (A)

$\sqrt{\frac{2}{3}}$

REF.Image

(1,0,1) $\to$ dr's of line

$cos\theta =\frac{1+0+1}{\sqrt{2}\sqrt{3}}=\sqrt{\frac{2}{3}}$

$AB=\sqrt{1+1}=\sqrt{2}$

projection = AB $sin\theta$

$=\sqrt{2}\sqrt{1-\frac{2}{3}}$

$=\sqrt{2}\sqrt{\frac{1}{3}}$

$=\sqrt{\frac{2}{3}}$