Write the equation of the plane ` vec r= vec a+lambda vec b+mu vec c\ ` in scalar product form.

Explanation

The given plane is `vec{r}=vec{a}+lambda vec{b}+mu c`.

So, it is clear from the given equation of plane, that the plane passing through a point `(vec{a})` and parallel to two vectors `vec{b}` and `vec{c}`.

So, the equation of the vector normal to the plane is given as,

`vec{n}=(vec{b} times vec{c})`

So, in scalar product form the vector equation of the plane is given as,

`(vec r-vec a)cdot vec n=0`


`implies (vec r-vec a)cdot (vec b-vec c)`

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