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

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'+bb'+cc'=0

B

(a+a')(b+b')+(c+c')=0

C

aa'+cc'+1=0

D

aa'+bb'+cc'+1=0

Text Solution

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The correct Answer is:
C
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NEW JOYTHI PUBLICATION-THREE DIMENSIONAL GEOMETRY-Objective
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  2. A unit vector parallel to the straight line (x-2)/3=(3+y)/(-1) = (z-2)...

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  3. The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d will be perpendicul...

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  4. If the vector equation of a line (x-2)/2=(2y-5)/(-3) =z+1 is vecr=2hat...

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  5. If the staight line (x-1)/k=(y-2)/2=(z-3)/3 and (x-2)/3=(y-3)/k =(z-1)...

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  6. The equation of the line joining the points (-3,4,11) and (1,-2,7) is

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  7. The vector equation of the line 6x-3=3y+4=2z-2 is

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  8. The angle between the staight lines (x+1)/2=(y-2)/5=(z+3)/4 and (x-1)/...

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  9. If the lines (x-1)/(-3)=(y-2)/(2k) =(z-3)/2 and (x-1)/(3k) =(y-5)/1=(z...

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  10. A line makes angles alpha,beta,gamma with the coordinates axes . If al...

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  11. The angle between the lines x=1,y=2 and y=-1 ,z=0 is

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  12. The distance between the lines vecr=veca1+tvecb and vecr=veca2+svecb i...

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  13. The vector equation of a plane which is at a distance of 6/sqrt29 from...

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  14. The equation of a plane with intercepts 2,3,and 4 on the x,y and z axe...

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  15. The direction cosines of the normal to the plane 6x-2y-2z=1 are

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  16. The distance of the point (2,1,-1) from the plane x-2y+4z=9 is

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  17. If the plane 2x-y+z=0 is parallel to the line (2x-1)/2=(2-y)/2 =(z+1)/...

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  18. The equation of the plane passing through (2,3,4) and parallel to the ...

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  19. The vector equation of the plane through the point (2,1,-1) and parall...

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  20. The equation of the plane passing through (1,2,3) and parallel to 3x-2...

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