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If a line makes angles. 90^@, 60^@, 30^@...

If a line makes angles. `90^@, 60^@, 30^@` with the x, y and z axes respectively,
find its direction cosines

Answer

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Knowledge Check

  • If a straight line makes the angle 60^(@),45^(@)andalpha with X, Y and Z-axes respectively, then "sin"^(2)alpha is equal to

    A
    `3/(4)`
    B
    `3/(2)`
    C
    `1/(2)`
    D
    1

  • 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

    A
    `75^(@)`
    B
    `30^(@)`
    C
    `45^(@)`
    D
    `60^(@)`

  • The equation of the straight line making angles 60^(@),60^(@)and45^(@) with positive direction of the coordinate axes and passing through the point (2,1,-1) is a) sqrt(2)(x-2)=sqrt(2)(y-1)=(z+1) b) (x-2)=sqrt(2)(y-1)=(z+1) c) sqrt(2)(x-2)=(y-1)=(z+1) d) (x-2)=sqrt(2)(y-1)=sqrt(2)(z+1)

    A
    `sqrt(2)(x-2)=sqrt(2)(y-1)=(z+1)`
    B
    `(x-2)=sqrt(2)(y-1)=(z+1)`
    C
    `sqrt(2)(x-2)=(y-1)=(z+1)`
    D
    `(x-2)=sqrt(2)(y-1)=sqrt(2)(z+1)`

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    Find equation of the line which makes intercepts -3 and 2 on the X and Y axes respectively. Find its slope.

    If alpha, beta, gamma are the directional angles that a line makes with x-axis, y-axis and z-axis respectively, then sin ^(2) a + sin ^(2) beta + sin ^(2) gamma =

    A line makes equal angles with the coordinate axis . Find the direction cosines.

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