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Prove that the straight lines whose dire...

Prove that the straight lines whose direction cosines are given by the relations `a l+b m+c n=0a n dfm n+gn l+hl m=0` are perpendicular, if `f/a+g/b+h/c=0` and parallel, if `a^2f^2+b^2g^2+c^2h^2-2a bfg-2b cgh-2a c hf=0.`

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RD SHARMA ENGLISH-DIRECTION COSINES AND DIRECTION RATIOS-All Questions
  1. If three mutually perpendicular lines have direction cosines (l1,m1,n...

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  2. Find the direction cosines of the sides of the triangle whose verti...

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  3. Prove that the straight lines whose direction cosines are given by ...

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  4. The x-coordinates of a point on t line joining the points Q(2,2,1)a...

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  5. Given that P(3,2,-4),Q(5,4,-6)a n dR(9,8,-10) are collinear. Find the ...

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  6. Find the coordinates of the foot of the perpendicular drawn from th...

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  7. Find the angle between the vectors with direction ratios proportion...

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  8. Determine the point in XY-plane which is equidistant from thee poin...

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  9. Find the angle between the lines whose direction cosines are given b...

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  10. Find the distance between the points A and B with position vectors hat...

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  11. Find the locus of the point which is equidistant from the points A(0...

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  12. Find the distance between the points P(-2,4,1) and Q(1,2,5).

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  13. Prove by using distance formula that the points P(1,2,3),Q(-1,-1,-1)a ...

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  14. Show that the points A(0,1,2),B(2,-1,3)a n dC(1,-3,1) are vertices of ...

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  15. Find the coordinates of a point equidistant from the four points O(...

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  16. Using vector method prove that the points A(6,−7,−1),B(2,−3,1) and C(...

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  17. Find the coordinates of the point which divides the joint of P(2,-1...

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  18. Find the ratio in which the line joining the points (1,2,3)a n d(-3...

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  19. Find the ratio in which the join the A(2,1,5)a n dB(3,4,3) is divided ...

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  20. Using distance formula prove that the following points are collinear: ...

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