Find the vector equation of the following planes in scalar product form `( vec rdot vec n=d): vec r=( hat i+ hat j)+lambda( hat i+2 hat j- hat k)+mu(- hat i+ hat j-2 hat k)`

Explanation

It is known that the equation `vec{r}=vec{a}+lambda vec{b}+mu vec{c}` represents a plane passing through a
point whose position vector is `vec{a}`

Now, `vec{a}=hat{1}-hat{j}`


`vec{b}=hat{1}+hat{j}+hat{k} `

`vec{c}=-4 hat{1}-2 hat{j}+3 hat{k}`


Normal vector, `vec{1}=vec{b} times c`

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