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A line AB in three-dimensional space mak...

A line AB in three-dimensional space makes angles `45^@` and `120^@` with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle q with the positive z-axis, then q equals

A

`30^@`

B

`45^@`

C

`60^@`

D

`75^@`

Text Solution

Verified by Experts

The correct Answer is:
C
`thereforecos^2""45^@+cos^2""120^@+cos^2theta=1`
`rArr" "1/2+1/4+cos^2theta=1`
`rArr" "cos^2theta=1-3/4=1/4`
`rArr" "costheta=1/2" "[thereforetheta" is acute"]`
`therefore" "theta=60^@`
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