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If a line marks angles alpha, beta and g...

If a line marks angles `alpha, beta and gamma` with the coordinates axes, prove that `sin^2alpha+sin^2beta+sin^2gamma=2`.

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PSEB-THREE DIMENSIONAL GEOMETRY-Exercise
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  4. If a line has the direction ratios –18, 12, – 4, then what are its dir...

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  5. Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear...

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  6. Find the direction cosines of the sides of the triangle whose vertices...

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  7. Show that the three lines with direction cosines 12/13, -3/13, -4/13, ...

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  8. Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perp...

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  9. Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel...

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  10. Find the equation of the line which passes through the point (1, 2, 3)...

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  11. Find the equation of the line in vector and in cartesian form that pas...

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  12. Find the cartesian equation of the line which passes through the point...

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  13. The cartesian equation of a line is (x-5)/3 = (y+4)/7 = (z-6)/2. Write...

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  14. Find the vector and the cartesian equations of the lines that passes t...

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  15. Find the vector and the cartesian equations of the line that passes th...

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  16. Find the angle between the following pair of lines: vecr = 2hati-5hatj...

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  17. Find the angle between the following pair of lines: vecr = 3hati+hatj-...

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  18. Find the angle between the lines [x-2]/2=[y-1]/5=[z+3]/-3 and [x+2]/-1...

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  19. Find the angle between the lines x/2=y/2=z/1 and [x-5]/4=[y-2]/1=[z-3]...

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  20. Find the values of p so that the lines (1-x)/3 = (7y-14)/2p = (z-3)/2 ...

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  21. Show that the lines (x-5)/7 = (y+2)/-5 = z/1 and x/1 = y/2 = z/3 are p...

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