- #1
mathmari
Gold Member
MHB
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Hey!
Find an equation for the plane that passes through $(3, 2, -1)$ and $(1, -1, 2)$ and that is parallel to the line $\overrightarrow{v}=(1, -1, 0)+t(3, 2, -2)$.
The general formula of the equation on the plane is $$Ax+By+Cz+D=0$$
where $(A, B, C)$ is a perpendicular.
Since the plane passes through $(3, 2, -1)$ and $(1, -1, 2)$ we have that
$$3A+2B-C+D=0 \\ A-B+2C+D=0 $$
Also $$(A, B, C) \cdot (3, 2, -2)=0 \Rightarrow 3A+2B-2C=0$$
Is this correct so far??
Find an equation for the plane that passes through $(3, 2, -1)$ and $(1, -1, 2)$ and that is parallel to the line $\overrightarrow{v}=(1, -1, 0)+t(3, 2, -2)$.
The general formula of the equation on the plane is $$Ax+By+Cz+D=0$$
where $(A, B, C)$ is a perpendicular.
Since the plane passes through $(3, 2, -1)$ and $(1, -1, 2)$ we have that
$$3A+2B-C+D=0 \\ A-B+2C+D=0 $$
Also $$(A, B, C) \cdot (3, 2, -2)=0 \Rightarrow 3A+2B-2C=0$$
Is this correct so far??