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Find the direction cosines of a line whi...

Find the direction cosines of a line which makes equal angles with the coordinate axes.

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Find the direction cosines of x,y and z axis.

A line passes through the points (6,-7,-1)a n d(2,-3,1)dot Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.

Knowledge Check

  • The direction cosines of a line that makes equal angles with the three axes in the space are

    A
    `pm1/sqrt3,pm1/3,pm1/3`
    B
    `pm1/sqrt3,pm1/sqrt3,pm1/sqrt3`
    C
    `pm6/7,pm2/7,pm3/7`
    D
    `pmsqrt(1/7), pmsqrt(3/14),pmsqrt(1/14)`

  • If the direction cosines of a line are k,k,k , then

    A
    k gt 0
    B
    0 lt k lt 1
    C
    k=1
    D
    `k=1/3` or `(-1)/sqrt3`

  • The direction cosines of a straight line, whose projections on the coordinate axes , OX, OY, OZ are 12,4,13 respectively , are

    A
    `12/29,4/29,13/29`
    B
    `12/sqrt329,4/sqrt329,13/sqrt329`
    C
    `1/12,1/4,1/3`
    D
    `12/329,4/329,13/329`

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    A plane passes through the point (-1,1,2) and the normal to the plane of magnitude 3sqrt3 makes equal acute angles with the coordinate axes. Find the equation of the plane.

    A plane passes through the point (1,1,2) - and the normal to the plane of magnitude 3sqrt(3) makes equal acute angles with the coordinate axes. Find the equation of the plane.

    Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

    Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

    A line with positive direction cosines passes through the point P(2, – 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

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