1. Vectors and Geometry

Lines And Planes — Quiz

Test your understanding of lines and planes with 5 practice questions.

Practice Questions

Question 1

Which of the following is the correct parametric form of a line passing through the point (1, 2, 3) with direction vector $ \mathbf{d} = \langle 4, -1, 2 \rangle $?

Question 2

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

Question 3

Find the intersection point of the line given by the parametric equations $ x = 1 + 2t $, $ y = 3 - t $, $ z = -2 + 4t $ and the plane $ x - y + 2z = 5 $. What is the value of $ t $ at the intersection?

Question 4

Which of the following is a vector parallel to the line given by the parametric equations $ x = -2 + 5s $, $ y = 3 + 4s $, $ z = 1 - s $?

Question 5

What is the angle between the two planes $ 3x - y + 2z = 7 $ and $ 2x + 4y - z = 3 $?