Chapter 10: Q. 34 (page 824)

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$
Find the area of the parallelogram determined by the vectors u and v.

Short Answer

Expert verified

The area of the parallelogram determined by the vectors u and vis $\sqrt{78}$ .

Step by step solution

Step 1. Given Information

The indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

We have to find the area of the parallelogram determined by the vectors u and v.

Step 2. Before finding area of the parallelogram determined by the vectors u and v we have to finding the cross product of u and v.

The cross product of $u \times v$

$u \times v = \det [\begin{matrix} i & j & k \\ - 3 & 1 & - 4 \\ 2 & 0 & 5 \end{matrix}]$

Now solving the determinant.

role="math" $u \times v = ((1) (5) - (- 4) (0)) i + ((- 3) (5) - (- 4) (2)) j + ((- 3) (0) - (1) (2)) k u \times v = (5 - 0) i + (- 15 + 8) j + (0 - 2) k u \times v = 5 i - 7 j - 2 k$

Step 3. The area of the parallelogram determined by u and v is u×v

$||u \times v|| = ||5 i - 7 j - 2 k|| ||u \times v|| = \sqrt{{(5)}^{2} + {(- 7)}^{2} + {(- 2)}^{2}} ||u \times v|| = \sqrt{25 + 49 + 4} ||u \times v|| = \sqrt{78}$

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.

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$
Find the area of the parallelogram determined by the vectors u and v.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Before finding area of the parallelogram determined by the vectors u and v we have to finding the cross product of u and v.

Step 3. The area of the parallelogram determined by u and v is u×v

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Geometry

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)Find the area of the parallelogram determined by the vectors u and v.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Before finding area of the parallelogram determined by the vectors u and v we have to finding the cross product of u and v.

Step 3. The area of the parallelogram determined by u and v is u×v

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Geometry

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$
Find the area of the parallelogram determined by the vectors u and v.