Find the distance between the point with position vector ` hat i-5 hat j-10 hat k` and the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/(12)` 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)`

putting value of r

in equation (2), we get,
`[(2i−j​+2k)+λ(3i+4j​+2k)[i−j​+k]=5`

`=>[(2+3λ)i+(4λ−1)j​+(2+2λ)k][i−j​+k]=5`

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