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A line makes angles `alpha,beta,gammaa n ddelta` with the diagonals of a cube. Show that `cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4//3.`

A

`2/3`

B

`4/3`

C

`8/3`

D

1

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The correct Answer is:
B
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ML KHANNA-CO-ORDINATE GEOMETRY OF THREE DIMENSION-PROBLEM SET (1)
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  2. A line line makes the same angle theta with each of the x and z-axes....

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  4. Which of the following triplets give the direction cosines of a line ?

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  7. If a line makes an angle (pi)/(4) with the positive directions of each...

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  8. A line passes through the point (6, -7, -1) and (2, -3, 1). The direct...

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  9. If P is a point in space such that OP is inclined to OX at 45^(@) and ...

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  10. The projections of a line segment on the coordinate axes are 12,4,3 re...

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  11. The direction cosines of the line joining the points (4,3,-5) and (-2,...

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  12. If (a,b,c) and (a^('),b^('),c^(') ) are the direction ratios of two pe...

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  13. If A(6,3,2), B(5,1,4), C(3,-4,7), D(0,2,5) be from points, the project...

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  14. The angle between the lines whose direction ratios are 1,1,2,sqrt3-1,-...

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  15. The angle between the lines 2x=3y=-z and 6x=-y=-4z is

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  16. Find the angle between the lines whose direction cosines are connec...

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  17. Three lines with direction cosines (1,1,2),(sqrt(3)-1,-sqrt(3)-1,4), (...

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  18. The co-ordinates of a point P are (3, 12, 4) with respect to origin O,...

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  19. The vertices of a triangle ABC are A(-1,2,-3),B(5,0,-6),C(0,4,-1). The...

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  20. The vertices of a triangles ABC are A(-1,2,-3),B(5,0,-6),C(0,4,-1).The...

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