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Prove that if the lines x = ay + b, z = ...

Prove that if the lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendiclar to each other aa' + cc' + 1 = 0.

A

`ac_1 + a_1 c = 1`

B

`"aa"_1 + "cc"_1 + 1 = 0`

C

`bc_1 + b_1c + 1 =0`

D

None of these

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The correct Answer is:
B
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-MULTIPLE CHOICE QUESTIONS (MCQs)
  1. The foot of perpendicular drawn from the point P(1,0,2) on the line (x...

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  2. The foot of perpendicular drawn from the point P(1,0,2) on the line (x...

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  3. Prove that if the lines x = ay + b, z = cy + d and x = a'y + b', z = c...

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  4. The lines (x-1)/(3) = (y-1)/(-1) = (z+1)/0 and (x-4)/(2) = (y+0)/(0) =...

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  5. The equation of motion of a point in space is x = 2t, y = -4 t, z=4t ...

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  6. The distance of the point P (4,3,5) from Y-axis is lambda then 5lambda...

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  7. A line makes an angle of measure alpha with X-axis and Y-axis cot alph...

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  8. The angle between the lines (x+1)/(2) + (y+3)/(2) = (z-4)/(-1) and (x-...

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  9. If the foot of perpendicular drawn from the point (a,b,c) and the line...

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  10. The distance between the lines x = 1 - 4t,y=2+ t, z= 3 + 2t and x=1 +S...

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  11. The distance ratio of two lines are (5,-12,13) and (-3,4,5) . Then the...

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  12. If cos alpha, cos beta, gamma are direciton cosines then cos 2 alpha +...

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  13. A line makes an angle alpha,beta and gamma with axes repectively, The ...

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  14. The angle between the lines 2x = 3y = -z and 6x = -y = -4x is ...........

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  15. Givne lines are (x-1)/(l) = (y + 1)/(m) = z/n and (x+1)/(m) = (y-3)/...

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  16. The distance of the point P(1,2,3) from the line (x-6)/(3) = (y-7)/(2)...

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  17. The lines x/1 = y/2 = z/3 and (x-1)/(-2) = (y-2)/(-4) = (z-3)/(-6)are ...

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  18. The direction ratios of the line x-y+z-5=0=x-3y-6 are

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  19. The shortest distance the lines (x-3)/(3) = (y-8)/(-1) = (z-3)/(1) and...

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  20. The direction cosines of line satisfy the relations lambda(l+m) = n an...

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