Question 1303a

Vectors II: Lines and Planes
Equation of a Plane from the Normal Vector

Question

The plane p{p} is given by
p:r(331)=29, p: \mathbf{r} \cdot \begin{pmatrix} 3 \\ - 3 \\ - 1 \end{pmatrix} = - 29,
Find the equation of the line l{l} that is perpendicular to p{p} and contains the point A(0,4,1).{A \left( 0, - 4, 1 \right).}

Attempt

l:{l: } r=a+λd,  λR.{\mathbf{r}=\mathbf{a}+\lambda\mathbf{d}, \; \lambda \in \mathbb{R}.}
a={\mathbf{a}=}
({\Biggl(}
),{\Biggr), \quad}
d={\mathbf{d}=}
({\Biggl(}
){\Biggr)}

Answer

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