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Let x-ysin alpha-zsin beta=0,xsin alpha+...

Let `x-ysin alpha-zsin beta=0`,`xsin alpha+zsin gamma-y=0` and `xsin beta+ysin gamma-z=0` be the equations of the planes such that `alpha+beta+gamma=pi//2` (where `alpha,beta` and `gamma!=0)dot` Then show that there is a common line of intersection of the three given planes.

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. If a line makes angles alpha,betaa n dgamma with three-dimensional c...

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  2. A plane which is perpendicular to two planes 2x-2y+z=0 and x-y+2z = 4 ...

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  3. Let x-ysin alpha-zsin beta=0,xsin alpha+zsin gamma-y=0 and xsin beta+y...

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  4. The position vectors of the four angular points of a tetrahedron OABC ...

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  5. Find the distance of the point (-2,3,-4) from the line ("x"+2)/3=(2"...

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  6. The plane 4x+7y+4z+81=0 is rotated through a right angle about its ...

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  7. If (a, b, c) is a point on the plane 3x + 2y + z = 7, then find the ...

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  8. Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z...

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  9. Let a1, a2, a3.......... be in A.P. and h1,h2,h3.....,in H.P. If a1=2 ...

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  10. If the angle between the plane x-3y+2z=1 and the line (x-1)/2=(y-1)/...

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  11. The length of projection of the line segment joining the points (1,...

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  12. Find the equation of a plane passing through (1, 1, 1) and parallel to...

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  13. Find the equation of the plane passing through the points(2,1,0),(5,0,...

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  14. Find the direction cosines of the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3),

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  15. The value of m for which straight lein 3x-2y+z+3=0=4 x-3y+4z+1 is pa...

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  16. Let the equations of a line and plane be (x+3)/2=(y-4)/3=(z+5)/2a n...

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  17. The length of the perpendicular form the origin to the plane passin...

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  18. In a three-dimensional xyz space, the equation x^(2)-5x+6=0 represents

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  19. The line (x-2)/3=(y+1)/2=(z-1)/-1 intersects the curve x y=c^(2),z=0 i...

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  20. A unit vector parallel to the intersection of the planes vec r. \ (...

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