Describe the relationship between the plane \(\mathbf{r}\cdot(3\mathbf{i}-2\mathbf{j}+4\mathbf{k})=2

Question

Describe the relationship between the plane $\mathbf{r}\cdot(3\mathbf{i}-2\mathbf{j}+4\mathbf{k})=2$ to the line $\frac{1-y}{2}=z,x=2$. Find the angle between the line and plane.

Accepted Answer

Line intersects plane at $\left(2,\frac32,-\frac14\right)$, $41.6^\circ$

Vectors - Relationships Between a Line and a Plane

Vectors - Relationships Between a Line and a Plane

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