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

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The correct Answer is:
`4/3`
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OMEGA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Questions
  1. A line makes angles alpha, beta, gamma, delta with the diagonals of a ...

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  2. If a line has direction ratios -18,12,-4, then what are its direction ...

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

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  4. A line passes through the point with position vector 2hat(i)-hat(j)+4h...

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

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

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  7. The vector equation of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2) is ........

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

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  9. Find the angle between the pair of line vec(r)=2hat(i)-5hat(j)+hat(k...

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  10. Find the angle between the pairs of lines vec(r)=3hat(i)+hat(j)-2hat...

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  11. Find the angle between the pair of lines (x+3)/3 = (y-1)/5 = (z+3)/4an...

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  12. Find the angle between the pair of lines (x-2)/2=(y-1)/5=(z+3)/(-3) an...

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  13. Find the angle between the lines (x)/(2)=(y)/(2)=(z)/(1) and (x-5)/(4)...

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  14. Find the angle between the lines (x+1)/(2)=(y)/(3)=(z-3)/(6) and the p...

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  15. The vector equation of two lines are vec(r)=hat(i)+2hat(j)+hat(k)+la...

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  16. Find the shortest distance between the lines whose vector equations ar...

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  17. Find the shortest distance between the following two lines vec(r)=(1+2...

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  18. The vector equation of two lines are vec(r)=(1-t)hat(i)+(t-2)hat(j)...

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  19. Find the equation of plane passing through (a,b,c) and parallel to the...

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  20. In the following cases, find the co-ordinates of the foot of the perpe...

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  21. In the following case, find the coordinates of the foot of the perpend...

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