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Prove that the measure of the angle betw...

Prove that the measure of the angle between two main diagonals of a cube is `cos^(-1)frac[1][3]`.

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The correct Answer is:
`((1)/(3))`
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ARIHANT PRAKASHAN-THREE DIMENSIONAL GEOMETRY -CHAPTER TEST
  1. Prove that the measure of the angle between two main diagonals of a cu...

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  2. If a line makes angles 90^(@), 135^(@), 45^(@) with the X, Y and Z-axe...

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  3. Find the direction cosines of the line segment joining the points A(7,...

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  4. Show that the points A(2, 3, -4), B(1, -2, 3) and C(3, 8, -11) are col...

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  5. If the x-coordinate of a point P on the join of Q(2,2,1) and R(3,8,11)...

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  6. Find the equation of a line parallel to X - axis and passing through ...

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  7. Find the equation of a plane that cuts the coordinate axes at (a, 0, 0...

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  8. Find the distance of the point whose position vector is (2hat(i) + hat...

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  9. Find the ratio in which the line segment through (2,4,5),(3,5,-4) is d...

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  10. State true or False .The planes 2x +4y -z + 1 = 0 and x - 2y - 6z + 3 ...

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  11. Find the equation of the plane .Passing through the point (2,3-1) and ...

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  12. State which of the following statements are true (T) or false(F) The...

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

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  14. A plane meets the coordinate axes at A, B and C respectivély. If the c...

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  15. Find the perpendicular distance of point (1,0,0) in from the lines (x-...

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  16. Show that the shortest distance between the lines x+a=2y=-12z and x=y+...

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  17. Find the equation of two planes through the origin, parallel to the li...

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  18. If a line makes angles alpha, beta  and gamma  with the positive direc...

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  19. Find the angle between the lines whose dcs. L, m, n are connected by t...

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  20. Bisecting the line segment joining (-1,4,3) and (5,-2,-1) at right ang...

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  21. Find the equation of the plane through the points (2, 2,1)and (9, 3, 6...

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