Find the vector and the Cartesian equation of the plane which pases through the point (5,2,-4) and perpendicular to the line with direction ratios (2,3,-1).

Explanation

Given:Plane passes through `(5,2,-4)`

So, `\vec{a}=5 \hat{\i}+2 \hat{\j}-4 \hat{k}`


Direction ratios of line perpendicular to the plane `=2,3,-1`

So,` \vec{n}=2 \hat{\i}+3 \hat{\j}-\hat{k}`

Equation of the plane in vector form is


`(\vec{r}-\vec{a}) \cdot \vec{n}=0`

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