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The line x/k=y/2=z/-12 makes an isoscel...

The line `x/k=y/2=z/-12` makes an isosceles triangle with the planes `2x+y+3z-1=0 and x+2y-3z-1=0` then the value of `k` is-

Text Solution

Verified by Experts

As the given line makes an isosceles triangle with the given planes, it means line is parallel to any one of the bisector of these planes.
Equation of bisector of these planes can be written as
`(2x+y+3z-1)/sqrt(2^2+1^2+3^2)=+-(x+2y-3z-1)/sqrt(1^2+2^2+3^2)`
`=>(2x+y+3z-1)/sqrt(14)=+-(x+2y-3z-1)/sqrt(14)`
`=>(2x+y+3z-1)=+-(x+2y-3z-1)`
For positive R.H.S
`x-y+6z=0->Eq(1)`
For negative R.H.S
...
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