Question 1303e

Vectors II: Lines and Planes
Cartesian and Vector Equation of a Plane

Question

Plane p{p} is given by the equation
p:r=(1−3−1)+λ(3−45)+μ(−432),  λ,μ∈R.p: \mathbf{r} = \begin{pmatrix} 1 \\ - 3 \\ - 1 \end{pmatrix} + \lambda \begin{pmatrix} 3 \\ - 4 \\ 5 \end{pmatrix} + \mu \begin{pmatrix} - 4 \\ 3 \\ 2 \end{pmatrix}, \; \lambda,\mu \in \mathbb{R}.
Express the equation of the plane p{p} in scalar product form r⋅n=k.{\mathbf{r}\cdot \mathbf{n} = k.}

Attempt

p:{p: }
r⋅{\mathbf{r}\cdot}
({\Biggl(}
){\Biggr)}
={=}

Answer

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