A line AB in three-dimensional space makes angles `45^o ` and `120^o`with the positive x-axis and the positive y-axisrespectively. If AB makes an acute angle q with the positivez-axis, then q equals
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`AB` makes angle `( alpha , beta, gamma) `with (x,y,z) axis
then, `cos^2 alpha + cos^2 beta + cos^2 gamma = 1`
`alpha = 45^@`
`beta= 120^@`
`(1/sqrt2)^2 + (-1/2)^2 + cos^2 gamma = 1`
`= cos^2 gamma = 1/4`
`cos gamma = 1/2or -1/2`
`cos gamma = 1/2`
`gamma = pi/3`
Answer