Dot product and angle in space Quiz
10 questions · easy to harder · Calculus 3 · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 2 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Calculate <1, 2, 3> • <4, −5, 6>Type the answer.
2 Question 2
Calculate <1, 1, 1> • <2, 3, 4>Type the answer.
3 Question 3
Dot product of <2, 3, −1> and <1, −1, 1>Type the answer.
4 Question 4
Calculate <−2, 5, 3> • <4, 1, −2>Type the answer.
5 Question 5
Dot product of <4, −2, 1> and <−1, 3, 5>Type the answer.
6 Question 6
Angle between <1, 0, 0> and <1, 1, 0>Type the answer.
7 Question 7
Angle between <2, 2, 1> and <1, 2, 2>- A) 27.3°
- B) 8°
- C) 273°
- D) 3°
8 Question 8
Angle between <3, 4, 0> and <0, 3, 4>Type the answer.
9 Question 9
Angle between <2, −1, 2> and <−2, 2, 1>- A) 3°
- B) −116.4°
- C) −4°
- D) 116.4°
10 Question 10
Angle between <1, 1, 1> and <1, −1, 2>Type the answer.