3. Geometry and Trigonometry

Vector Equations Of Planes — Quiz

Test your understanding of vector equations of planes with 5 practice questions.

Practice Questions

Question 1

Which expression gives the vector equation of a plane that passes through the point with position vector $\mathbf{a}$ and has normal vector $\mathbf{n}$?

Question 2

Which vector is a normal vector to the plane with equation $(\mathbf{r}-\mathbf{a})\cdot(2, -3, 1)=0$?

Question 3

A plane passes through the point $(1,2,3)$ and has normal vector $(4,0,-2)$. Which equation represents the plane?

Question 4

If a plane has equation $(\mathbf{r}-\mathbf{a})\cdot\mathbf{n}=0$, what does the vector $\mathbf{r}-\mathbf{a}$ represent?

Question 5

Which statement is true about two planes whose normal vectors are parallel?