Cross product and area 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.
- 5 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>- A) (3, −6, 3)
- B) (−3, 6, −3)
- C) (−3, −6, −3)
- D) (3, 6, −3)
2 Question 2
Calculate <2, 1, 0> × <0, 3, 1>Type the answer.
3 Question 3
Calculate <2, 3, 1> × <1, 1, 2>- A) (5, −3, −1)
- B) (5, 3, −1)
- C) (−5, −3, −1)
- D) (−5, 3, 1)
4 Question 4
Calculate <−1, 2, 4> × <3, 0, −2>Type the answer.
5 Question 5
Cross product of <0, 2, −1> and <3, 1, 2>- A) (−5, 3, 6)
- B) (5, 3, −6)
- C) (−5, −3, −6)
- D) (5, −3, −6)
6 Question 6
Find the area of the parallelogram with sides <1, 2, 2> and <2, 1, −2>.Type the answer.
7 Question 7
Find the area of the parallelogram with sides <2, 0, 0> and <0, 3, 4>.- A) 0
- B) 6
- C) 10
8 Question 8
Find the area of the triangle with corners (1, 0, 0), (0, 2, 0), (0, 0, 3).Type the answer.
9 Question 9
Find the area of the triangle with corners (1, 1, 1), (2, 3, 1), (1, 2, 3).- A) A ≈ 2.3
- B) A ≈ 23
- C) A ≈ 1
- D) A ≈ 4
10 Question 10
Calculate <1, 2, −3> × <2, 4, 1>Type the answer.