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A line makes an obtuse angle with the po...

A line makes an obtuse angle with the positive X-axis and angle `pi/4 and pi/3` with positive Y and Z-axes respectively. Its directions cosines are

A

`((-1)/sqrt2,1/sqrt2,1/2)`

B

`((1)/sqrt2,1/sqrt2,1/2)`

C

`(-(1)/2,1/sqrt2,1/2)`

D

`((1)/2,1/sqrt2,1/2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `m=cos""pi/4=1/sqrt2 and n=cos""pi/3=1/2`
`therefore" "l^2+m^2+n^2=1`
`rArr" "l=sqrt(1-(m^2+n^2))`
`=sqrt(1-(1/2+1/4))=sqrt(1-3/4)`
`rArr" "l=pm1/2`
Since, line makes an obtuse angle with X-axis so we take
`therefore` Direction cosines are `(-1/2,1/sqrt2,1/2)`
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