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The angle between the line x/2 = y/3 = ...

The angle between the line ` x/2 = y/3 = z/4` and the plane 3 x + 2y -3z =4 is

A

`45^(@)`

B

`0^(@)`

C

`cos^(-1) (24/(sqrt(29)sqrt(22)))`

D

`90^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have direction ratio of line M
` x/2, y/3, z/4 " is " (2,3,4) ` are plane
3x + 2y -3y =4 is ( 3,2,-3)
Angle between line and plane is
` sin theta = ((2)(3) + (3)(2)+ (4) (-3))/((sqrt(2^(2)+3^(2) +4^(2))(sqrt(3^(2)+2^(2)+(-3)^(2)))`
` sin theta= (6+6-12)/((sqrt(29)(sqrt(32)))=0`
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