Q. 9 Sketch the parallelogram determi... [FREE SOLUTION]

Chapter 10: Q. 9 (page 823)

Sketch the parallelogram determined by the two vectors $(1, 2)$ and $(3, 鈭� 1)$ . 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 $(3, 鈭� 1)$ . 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

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

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

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

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

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91影视

Sketch the parallelogram determined by the two vectors $(1, 2)$ and $(3, 鈭� 1)$ . 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

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91影视

Sketch the parallelogram determined by the two vectors (1,2)and (3,鈭�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

Geometry

Mechanics Maths

Applied Mathematics

Calculus

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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