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A line makes angles of measures (pi)/(6)...

A line makes angles of measures `(pi)/(6)` and `(pi)/(3)` with X-and Z-axes respectively. Find the angle made by the line with the Y-axis.

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To solve the problem, we need to find the angle made by a line with the Y-axis, given that it makes angles of \(\frac{\pi}{6}\) with the X-axis and \(\frac{\pi}{3}\) with the Z-axis. ### Step-by-Step Solution: 1. **Define the Angles**: Let the angles made by the line with the X, Y, and Z axes be denoted as \(\alpha\), \(\beta\), and \(\gamma\) respectively. According to the problem: - \(\alpha = \frac{\pi}{6}\) (angle with X-axis) - \(\gamma = \frac{\pi}{3}\) (angle with Z-axis) ...
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Knowledge Check

  • If a line makes angles (pi)/(3) and (pi)/(4) with X-axis and Y-axis respectively, then the angle made by the line with Z-axis is

    A
    `(pi)/(2)`
    B
    `(pi)/(3)`
    C
    `(pi)/(4)`
    D
    `(5pi)/(12)`

  • If a line makes angle (pi)/3 and (pi)/4 with x-axis and y-axis respectively then the angle made by the line with z-axis, is

    A
    `(pi)/2`
    B
    `(pi)/3`
    C
    `(pi)/4`
    D
    `(5pi)/12`

  • If a line makes angles of 30^(@) and 45^(@) with X-axis and Y-axis respectively, then the angle made by it with Z-axis is

    A
    `45^(@)`
    B
    `60^(@)`
    C
    `120^(@)`
    D
    does not exist

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