The distance of the point `(1,-2,3)` from the plane `x-y+z=5` measured parallel to the line `x/2=y/3=z/-6`, is

Explanation

Point `A=(1,-2,3) \rightarrow(x_{1}, y_{1}, z_{1})`


Equation of plane: `x-y+z=5`


Equation of line: `\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}`
`(1)`


Equation of line passing through point `A`:


`\frac{x-x_{1}}{a} &=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}`
`(2)`


a, b, c `\rightarrow` direction cosines


The direction cosines of `(1)` and `(2)` are same since they are parallel.


`a=2, b=3, c=-6`


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