Find the distance of the point `P(-1,-5,-10)` from the point of intersection of the line joining the points `A(2,-1,2)a n dB(5,3,4)` with the plane `x-y+z=5.`

Explanation

The equation of the given line is

`r=(2i^−j^​+2k^)+λ(3i^+4j^​+2k^).....(1)`

The equation of the given plane is

`r.(i^−j^​+k^)=5........(2)`

Substituting the value of r
in equation (2), we get,

`[(2i^−j^​+2k^)+λ(3i^+4j^​+2k^)][i^−j^​+k^]=5`


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