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

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ARIHANT PUBLICATION-THREE-DIMENSIONAL GEOMETRY-Chapter Practice
  1. A line makes angles alpha, beta, gamma, delta with the four main diago...

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  2. The x-coordinate of a point on the line joining the points P(2,2,1) an...

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  3. Find the direction cosines of the line passing through two points (-2,...

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  4. If a line has direction ratios 2, -1, 2, then determine its direction ...

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  5. If P is a point in space such that OP = 12 and OP is inclined at angle...

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  6. Show that the lines (x-5)/(7) = (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)...

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  7. What is the angle between two planes 3x - 4y + 5z = 0 and 2x - y - 2z ...

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  8. Write the direction cosines of the normal to plane 3x+4y +12z = 52

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  9. Find the cartesian equation of the plane vec(r).[(s-2t) hat(i) + (3-t)...

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  10. What is the cartesian equation of the line vec(r)=(3hat(i) - hat(j) + ...

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  11. Write the vector equation ofthe line given by (x - 5)/3 = (y + 4)/7 = ...

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  12. Cartesian equation of line AB is (2x-1)/(2) = (4-y)/(7) = (z+1)/(2). W...

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  13. Find the equation of line passing through the point (2, 1, 3) having t...

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  14. Find the equation of a line parallel to Y-axis and passing through the...

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  15. Find the coordinates of the point, where the line passing through (5, ...

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  16. Write the condition for the lines vec(r) = vec(a)(1) + lambda vec(b)(1...

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  17. Find the equation of the plane passing through the point(-1,-1, 2) and...

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  18. Find the equation of the plane passing through the intersection of the...

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  19. Find the vector and cartesian equation of the line passing through the...

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  20. Find the vector equation of the plane determined by the points A(3,-1,...

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  21. Find the coordinates of the point where the line through the points A(...

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