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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:
B
`sintheta=((a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))/(sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2))sqrt(a_(1)^(2)+b_(2)^(2)+c_(2)^(2))))`
`(2xx3+3xx2-4xx3)/(sqrt(2^(2)+3^(3)+4^(2))sqrt((3)^(2)+(2)^(2)+(-3)^(2)))`
`=(6+6-12)/(sqrt(4+9+16)sqrt(9+4+9))=0`
`rArr" "theta=0^(@)`
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