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Prove that the lines x=az+b,y=cz+d and x...

Prove that the lines `x=az+b,y=cz+d` and `x=a_1z + b_1,y=c_1z+d_1 ` are perpendicular if `aa_1+"cc"_1+1=0.`

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ARIHANT PRAKASHAN-THREE DIMENSIONAL GEOMETRY -TOPIC TEST 3
  1. Find the cartesian equation of the line which passes through the point...

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  2. The equation of straight line equally inclined to the axes and equidis...

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  3. Find the equation of lines joining the points. (a,a,a) and (a,0,a)

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  4. Find the symmetric form of equation of the lines x + 2y + z - 3 = 0 = ...

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  5. Prove that the lines (x + 3)/(-3) = (y - 1)/(1) = (z - 5)/(5) and (x +...

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  6. Find the angle between the plane x+y+4=0 and the line (x+3)/2=(y-1)/1=...

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  7. Find the acute angle between the lines passing through (-3, -1, 0), (2...

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  8. Prove that the lines x=az+b,y=cz+d and x=a1z + b1,y=c1z+d1 are perpen...

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  9. Find the angle between the lines (x - 3)/(1) = (y - 2)/(2) = (z + 4)/(...

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  10. For what value of k lines (x + 2)/(-k) = (y - 3)/(2) = (z + 4)/(k) and...

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  11. Show that the lines (x - 5)/(4) = (y - 7)/(4) = (z + 3)/(-5) and (x - ...

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  12. Find the coordinates of the point, where the line (x+1)/(2) = (y+2)/(3...

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  13. Find the distance of the point (2, 3, 4) from the plane 3x + 2y + 2z+ ...

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  14. Find the length and the foot of perpendicular drawn from the point (2,...

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  15. Find the vector and cartesian equations of line passing through the po...

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  16. Cartesian equation of line AB is (2x-1)/(2) = (4-y)/(7) = (z+1)/(2). W...

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  17. Find the co-ordinates of the point where the line joining (3,4,-5) and...

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  18. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

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  19. Find equation of a plane through (2,-3,1) and perpendlcular to the lin...

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  20. Find the equation of the plane containg the line x + 2 = 2y - 1 = 3z a...

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