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A line makes angles angle, beta, gamma a...

A line makes angles `angle, beta, gamma and delta` with the diagonals of a cube. Show that `cos^(2)alpha+cos^(2)beta+cos^(2)gamma+cos^(2)delta=4//3`.

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RD SHARMA ENGLISH-DIRECTION COSINES AND DIRECTION RATIOS-All Questions
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  2. Find the angel between the vectors with direction ratios proportion...

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  3. Write the distance of the point P(2,3,5) from the xy-plane.

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  4. Write the coordinates the reflections of point (3,\ 5) in X and Y -...

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  5. Find the distance of the point (2, 3, 4) from the x- axis.

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  6. If a line has direction ratios proportional to 2, -1, -2, then what...

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  7. Write the direction cosines of a line parallel to z-axis.

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  8. If a unit vector vec a makes angles pi/3 with hat i ,pi/4 with hat ...

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  9. For every point P(x ,\ y ,\ z) on the xy-plane, a. x=0 b. y=0 c. ...

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  10. For every point (x\ , y ,\ z) on the x- axis (except the origin) a....

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  11. A rectangular parallelepiped is formed by planes drawn through the p...

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  12. A parallelepiped is formed by planes drawn through the points (2, 3...

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  13. The xy-plane divided the line joining the points(-1, 3, 4) and (2, -5,...

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  14. If the x-coordinate of a point P on the join of Q(2, 2, 1) and R(5, 1,...

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  15. The length of the perpendicular drawn from the point P(a , b , c) from...

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  16. Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2...

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  17. If P (3,2,−4) , Q (5,4,−6) and R (9,8,−10)  are collinear, then  ...

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  18. If O is the origin, OP = 3, with direction ratios -1, 2 and -2, then f...

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  19. Show that the angle between two diagonals of a cube is cos^(-1)sqrt(1/...

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  20. A line makes angles angle, beta, gamma and delta with the diagonals of...

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