Find the equation of line passing through points `A(0,6,- 9) and B(-3,- 6,3).` If D is the foot of perpendicular drawn from the point `C (7,4,-1)` on the line `AB,` then find the coordinates of point D and equation of line `CD.`

Explanation

It is known that, equation of line passing through the points `(x_{1}, y_{1}, z_{1})` and `(x_{2}, y_{2}, z_{2})` is given by


`frac{x-x_{1}}{x_{2}-x_{1}}=frac{y-y_{1}}{y_{2}-y_{1}}=frac{z-z_{1}}{z_{2}-z_{1}}`


Here, `A(x_{1}, y_{1}, z_{1})=(0,6,-9)`

and
therefore, Equation of line {AB} is given by


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