Chapter 10: Q. 28 (page 824)

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$
Find the area of the parallelogram determined by the vectors v and w.

Short Answer

Expert verified

The area of the parallelogram determined by the vectors v and w is $\sqrt{1096}$ .

Step by step solution

Step 1. Given Information

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

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

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

The cross product of $v \times w$

role="math" localid="1649414070213" $v \times w = \det [\begin{matrix} i & j & k \\ 4 & 0 & 1 \\ - 2 & 6 & 5 \end{matrix}] Now solving the determinant . v \times w = ((0) (5) - (1) (6)) i + ((4) (5) - (1) (- 2)) j + ((4) (6) - (0) (- 2)) k v \times w = (0 - 6) i + (20 + 2) j + (24 + 0) k v \times w = - 6 i + 22 j + 24 k$

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

$||v \times w|| = ||- 6 i + 22 j + 24 k|| ||v \times w|| = \sqrt{{(- 6)}^{2} + {(22)}^{2} + {(24)}^{2}} ||v \times w|| = \sqrt{36 + 484 + 576} ||v \times w|| = \sqrt{1096}$

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In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$
Find the area of the parallelogram determined by the vectors v and w.

Short Answer

Step by step solution

Step 1. Given Information

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

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

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In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)Find the area of the parallelogram determined by the vectors v and w.

Short Answer

Step by step solution

Step 1. Given Information

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Logic and Functions

Statistics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$
Find the area of the parallelogram determined by the vectors v and w.