Chapter 10: Q. 9 (page 823)

Sketch the parallelogram determined by the two vectors $(1, 2)$ and $(3, - 1)$ . How can you use the cross product to find the area of this parallelogram?

Short Answer

Expert verified

The area of this parallelogram is $7$ .

Step by step solution

Step 1. Given Information

Sketch the parallelogram determined by the two vectors $(1, 2)$ and $(3, - 1)$ . We have to use the cross product to find the area of this parallelogram.

Step 2. Sketch the parallelogram determined by the two vectors (1,2) and (3,-1) is

Step 3. Now the vectors are (1,2,0) and (3,-1,0).

Now the cross product is

$u \times v = \det [\begin{matrix} i & j & k \\ 1 & 2 & 0 \\ 3 & - 1 & 0 \end{matrix}]$

role="math" localid="1649266998375" $u \times v = ((0) (2) - (- 1) (0)) i + ((1) (0) - (3) (0)) j + ((1) (- 1) - (2) (3)) k u \times v = (0 + 0) i + (0 - 0) j + (- 1 - 6) k u \times v = 0 i + 0 j - 7 k$

Step 4. The area of the parallelogram determined by u and v is

$||u \times v|| = ||0 i + o j - 7 k|| ||u \times v|| = \sqrt{0^{2} + 0^{2} + {(- 7)}^{2}} ||u \times v|| = \sqrt{49} ||u \times v|| = 7$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Sketch the parallelogram determined by the two vectors $(1, 2)$ and $(3, - 1)$ . How can you use the cross product to find the area of this parallelogram?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Sketch the parallelogram determined by the two vectors (1,2) and (3,-1) is

Step 3. Now the vectors are (1,2,0) and (3,-1,0).

Step 4. The area of the parallelogram determined by u and v is

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Sketch the parallelogram determined by the two vectors (1,2)and (3,−1). How can you use the cross product to find the area of this parallelogram?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Sketch the parallelogram determined by the two vectors (1,2) and (3,-1) is

Step 3. Now the vectors are (1,2,0) and (3,-1,0).

Step 4. The area of the parallelogram determined by u and v is

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Sketch the parallelogram determined by the two vectors $(1, 2)$ and $(3, - 1)$ . How can you use the cross product to find the area of this parallelogram?