A line `AB` in three-dimensional space makes angles `45^@` and `120^@` with the positive`x`-axis and the positive `y`-ax

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Q 1124680551.     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 theta with the positive `z`-axis, then theta equals
JEE 2010 Mains
A

`45^@`

B

`60^@`

C

`75^@`

D

`30^@`

HINT

For a line with direction cosines `cos alpha, cos beta, cos gamma`, (where `alpha` is angle made by the line with the positive `x`-axis, `beta` with the positive `y`-axis, and gamma with the positive `z`-axis) we have: `cos^2 alpha + cos^2 beta + cos^2 gamma = 1`

Solution
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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