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If a line is inclined at 60^(@) and 30^(...

If a line is inclined at `60^(@)` and `30^(@)` with the X-and Y-axes respectively, then the angle which makes with the Z-axes is

A

0

B

`(pi)/(4)`

C

`(pi)/(2)`

D

`(pi)/(6)`.

Text Solution

AI Generated Solution

To find the angle that a line makes with the Z-axis when it is inclined at \(60^\circ\) with the X-axis and \(30^\circ\) with the Y-axis, we can use the relationship between the angles and the cosines of those angles. ### Step-by-step Solution: 1. **Understand the relationship**: The angles that a line makes with the X, Y, and Z axes are denoted as \(\theta_1\), \(\theta_2\), and \(\theta_3\) respectively. According to the formula: \[ \cos^2 \theta_1 + \cos^2 \theta_2 + \cos^2 \theta_3 = 1 \] ...
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Knowledge Check

  • 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

  • If a line makes angles 60^(@) and 45^(@) with the Y and Z-axes respectively, then the direction cosines of the line are

    A
    `pm(1)/(2),(1)/(2),(1)/(sqrt(2))`
    B
    `pm(1)/(2),(sqrt(3))/(2),(1)/(sqrt(2))`
    C
    `pm(1)/(sqrt(2)),(1)/(2),(1)/(2)`
    D
    `pm(sqrt(3))/(2),(1)/(2),(1)/(sqrt(2))`

  • If a line makes angle 120^(@) and 60^(@) with the positive directions of X and Z-axes respectively, then the angle made by theline with positive Y-axis is

    A
    `150^(@)`
    B
    `60^(@)`
    C
    `135^(@)`
    D
    `120^(@)`

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    Let A(-1, 2, 1) and B(4, 3, 5) be two given points. Find the projection of AB on a line which makes angle 120^(@) and 135^(@) with Yand Z-axes respectively, and an acute angle with X-axis.

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    If a vector vecA makes angles 45^(@) and 60^(@) with x and y axis respectively then the angle made by it with z-axis is

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