6. Geometry and Vectors

3d Geometry — Quiz

Test your understanding of 3d geometry with 5 practice questions.

Practice Questions

Question 1

What is the formula for the distance between two points $A(x_1, y_1, z_1)$ and $B(x_2, y_2, z_2)$ in three-dimensional space?

Question 2

Which of the following is the equation of a plane that passes through the point $(1, 2, 3)$ and is perpendicular to the vector $\mathbf{n} = \langle 2, -1, 4 \rangle$?

Question 3

What is the angle between the two vectors $\mathbf{a} = \langle 1, 2, 2 \rangle$ and $\mathbf{b} = \langle 2, 0, 1 \rangle$?

Question 4

If a line in three-dimensional space passes through the point $(1, -2, 3)$ and has direction vector $\langle 4, 2, -1 \rangle$, what is the parametric equation of the line?

Question 5

What is the volume of a tetrahedron formed by the points $A(0, 0, 0)$, $B(1, 0, 0)$, $C(0, 1, 0)$, and $D(0, 0, 1)$?