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Write the angle between the line (x-1)/2...

Write the angle between the line `(x-1)/2=(y-2)/1=(z+3)/-2` and the plane `x+y+4=0`.

A

`0^(@)`

B

`30^(@)`

C

`45^(@)`

D

`90^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Direction ratio of the line and the normal to the plane are 2,1,-2 and 1,1,0 respectively.
`:.` Their direction cosines are
`2/3,1/2,-2/3`
and `1/(sqrt(2)),1/(sqrt(2)),0`
If `theta` is the angle between theline and the plane then
`cos (90^(@)-theta)=2/3xx1/(sqrt(2))+1/3xx1/(sqrt(2))+(-2/3)xx0`
`impliessin theta=1/(sqrt(2))`
`implies theta=45^(@)`
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