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If a line makes angles 90o," "135o," ...

If a line makes angles `90o," "135o," "45o` with the x, y and z-axes respectively, find its direction cosines.

Text Solution

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The correct Answer is:
`lt 0,- (1)/(sqrt(2)), (1)/(sqrt(2)) gt `
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If a line makes angles 90^(@),135^(@),45^(@) with the x,y and z -axes respectively,find its direction cosines.

(A) If a line makes angle 90^(@), 135^(@), 45^(@) with the x , y and z respectively, find its direction-cosines. (b) If a line has direction-ratio lt 2, -1, -2, gt , determine its direction-cosines.

Knowledge Check

  • 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
    `(1)/(sqrt(2)),0,(1)/(2)`
    D
    `(1)/(2),0,(1)/(sqrt(2))`

  • 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 the line makes angles 45^(@), 60^(@), 120^(@) with X, Y, Z axes respectively, then the direction consines of line are

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

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    If a line makes angles 90^@, 135^@, 45^@ with X,Y and Z axes respectively , then find its direction cosines.

    If a line makes angle 90o , 60o and 30o with the positive direction of x, y and z-axis respectively, find its direction cosines.

    If line makes angles of 90,135,45 with coordinate axis respectively, then its direction cosines are (1) (2) (3) (4)

    Can a line make angle 45^(@), 60^(@), 120^(@) with x-,y- and z-axes respectively.

    Of line makes angle 60^(@), 120^(@), 45^(@) with X, Y, Z axes respectively, then the direction consines of a line are

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