Three Dimensional Geometry Question 388
Question: The length of projection of the line segment joining the points $ ( 1,0,-1 ) $ and $ ( -1,2,2 ) $ on the plane $ x+3y-5z=6 $ is equal to
Options:
A) 2
B) $ \sqrt{\frac{271}{53}} $
C) $ \sqrt{\frac{472}{31}} $
D) $ \sqrt{\frac{474}{35}} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Let $ A( 1,0,,-1 ),B( -1,2,2 ) $ Direction ratios of segment AB are $ <2,-2,-,3>. $
$ \therefore ,\cos \theta \frac{| 2\times 1+3(-2)-5(-,3) |}{\sqrt{1+9+25},\sqrt{4+4+9}} $ $ =\frac{11}{\sqrt{17}\sqrt{35}} $ $ =\frac{11}{\sqrt{595}} $ Length of projection $ =(AB)sin\theta $ $ =\sqrt{(2^{2})+{{(2)}^{2}}+{{(3)}^{2}}}\times \sqrt{1-\frac{121}{595}} $ $ =\sqrt{17}\frac{\sqrt{474}}{\sqrt{17}\sqrt{35}} $ $ =\sqrt{\frac{474}{35}} $ Units
BETA
