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Verify that <(l1+l2+l3)/sqrt3,(m1+m2+m3)...

Verify that `<(l_1+l_2+l_3)/sqrt3,(m_1+m_2+m_3)/sqrt3,(n_1+n_2+n_3)/sqrt3>` can be taken as the direction cosines of a line L equally inclined to three mutually perpendicular lines with direction cosines: `, , `

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

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  2. Using converse of Basic Proportionality theorem prove that the line jo...

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  3. Verify that <(l1+l2+l3)/sqrt3,(m1+m2+m3)/sqrt3,(n1+n2+n3)/sqrt3> can b...

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  4. Find the vector equation of the line passing through (1, 2, 3) and per...

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  5. The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular ...

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  6. Prove that the line joining the points vec(6a)-vec(4b)+vec(4c) and -ve...

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  7. Find the vector equation of the line passing through (1, 2, 3) and par...

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  8. Find the vector equation of the line passing through the point (1,2,-4...

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  9. Find the co-ordinates of the points where the line through the points ...

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  10. Show that the equation of the plane passing through a point having pos...

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  11. Find the distance of the point (2,1,0) from the plane 2x+y+2z+5=0.

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  12. Find the distance of the point with position vector -hati-5hatj-10hatk...

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  13. Find the point, where the line joining the points (1,3,4) and (-3,5,2)...

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  14. Find the equation of the plane passing through the line of intersectio...

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  15. If from a point P(a,b,c) perpendicular PA and PB are drawn to yz and z...

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  16. If O be the origin and the coordinates of P be (1, 2, – 3), then find ...

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  17. Find the equation of the plane which contains the line of intersection...

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  18. Prove that the S.D. between a diagonal of a rectangular parallelopiped...

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  19. What is the equation of the xy-plane?

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  20. If a line makes an angle alpha, beta, gamma with x axis, y axis and z ...

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