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If the lines x=ay +b, z=cy+d and x=a'y...

If the lines
x=ay +b, z=cy+d and `x=a'y + b', z=c'y + d'` are perpendicular, then

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

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the two lines x=ay+b,z=cy+d and x=a\'y+b,z=c\'y+d\' will be perpendicular, if and only if: (A) aa\'+cc\'=1=0 (B) aa\'+bb\'+cc\'=1=0 (C) aa\'+bb\'+cc\'=0 (D) (a+a\')+(b+b\')+(c+c\')=0

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MOTION-THREE DIMENSIONAL GEOMETRY (3 -D)-SOLVED EXAMPLE
  1. Show that the origin lies in the acute angles between the planes x + 2...

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  2. The cartesian equation of a line is (x-3)/(2)=(y+1)/(-2)=(z-3)/(5). Fi...

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  3. If the lines x=ay +b, z=cy+d and x=a'y + b', z=c'y + d' are perpendi...

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  4. Find the coordinates of the foot of the perpendicular drawn from po...

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  5. Find the shortest distance between the lines vecr=(hatii+2hatj+hatk)+l...

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  6. Show that the disease of the point of intersection of the line (x-2)/3...

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  7. Find the co-ordinates of the foot of the perpendicular drawn from the ...

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  8. The equation of straight line 3x + 2y - 2-4 = 0 ; 4x+y-2z + 3 = 0 in ...

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  9. Find the equation of the plane through the intersection of the planes ...

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  10. Find the equation of a plane passing through the line (x-1)/1=(y-2)/1=...

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  11. Prove that the lines 3x + 2y + z – 5 = 0 = x + y – 2z – 3 and 2x – y –...

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  12. Find the equation of the plane which contains the two parallel lines ...

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  13. Find the distance of the point P(3,8,2) from the line 1/2(x-1)=1/4(...

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  14. Find the intersection of the line joining the points (1, –2,–1) and (2...

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  15. Equation of line of projection of the line 3x-y+2z-1=0=x+2y-z-2 on the...

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  16. Find the equation of the projection of the line (x-1)/2=(y+1)/(-1)=...

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  17. Find the foot and hence the lengh of perpendicular form (5,7,3) to the...

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  18. Show that the planes 2x – 3y – 7z = 0, 3x – 14y – 13z = 0, 8x – 31y – ...

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  19. Value of lambda do the planes x-y+z+1=0, lambdax+3y+2z-3=0, 3x+lambday...

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  20. The equation of the line passing through (1, 1, 1) and perpendicular t...

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