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If a line makes angle 120^(@) and 60^(@)...

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^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let angles `alpha,beta,gamma` makes positive direction of X,Y and Z-axes, respectively.
`thereforecos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
Here, `alpha=120^(@) and gamma=60^(@)`
`thereforecos^(2)120^(@)+cos^(2)beta+cos^(2)60^(@)=1`
`implies((1)/(2))^(2)+cos^(2)beta+((1)/(2))^(2)=1`
`impliescos^(2)beta=1-(1)/(2)=(1)/(2)`
`impliescosbeta=(+-(1))/(sqrt(2))`
`impliesbeta=135^(@)`
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Knowledge Check

  • If a line makes angles of measure 45^(@) and 60^(@) with the positive direction of the Y and Z axex respectively, then the angle made by the line with the positive directions of the X-axis is

    A
    `30^(@)" or " 150^(@)`
    B
    `30^(@)" or " 120^(@)`
    C
    `60^(@)" or " 120^(@)`
    D
    `60^(@)" or " 150^(@)`

  • A line makes angles of 45^(@) and 60^(@) with the positive axes of X and Y respectively. The angle made by the same line with the positive axis of Z is

    A
    `30^(@) or 60^(@)`
    B
    `60^(@) or 90^(@)`
    C
    `90^(@) or 120^(@)`
    D
    `60^(@) or 120^(@)`

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

    A
    `(1)/(sqrt(2)),(1)/(2),(1)/(2)`
    B
    `0,(1)/(2),(1)/(2)`
    C
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    D
    `(1)/(2),0,(1)/(sqrt(2))`

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