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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'` are pendicular to each other if

A

`cc' + a + a' = 0`

B

`bb' + cc' + 1 = 0`

C

`ab' + bc' + 1 = 0`

D

`aa' + c + c' = 0`

Text Solution

Verified by Experts

The correct Answer is:
D
`{:(x-ay-b=0),(cy-z+d=0):}} and {:(x-a'z-b'=0),(y-c'z-d'=0):}`
The vector along the line of intersection of first two planes is given by
`|(veci,j,hatk),(1,-a,0),(0,c,-1)|=veci(a)+j+hatk(c )`
The vector along the line of intersection of the last two planes is
`|(veci,j,hatk),(1,0,-a'),(0,1,-c')|=veci(a')+j(c')+hatk(1)`
The lines will be perpendicular if : `aa'+c'+c=0`
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