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Prove that the lines, whose direction co...

Prove that the lines, whose direction cosines are given by `al+bm+cn=0, fmn+gnl+hlm=0` are: perpendicular if `f/a+g/b+h/c=0`

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Show that the sequence t n defined by t n = 3 n + 1 is an AP.

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  2. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

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  3. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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