Chapter 9: Q. 47 (page 627)

In Problem, find the area of the parallelogram with one corner at P1 and adjacent sides
$\vec{P 1 P 2} a n d \vec{P 1 P 3}$
$P 1 = (1, 2, 0), P 2 = (- 2, 3, 4), P 3 = (0, - 2, 3)$

Short Answer

Expert verified

The area of the parallelogram is : $\sqrt{555}$

Step by step solution

Step1. Giving information

three points $P 1 (1, 2, 0), P 2 (- 2, 3, 4), P 3 (0, - 2, 3)$

We know that the vector is formed by two points like

A = ({x_{2} - x}_{1}) i + (y_{2} - y_{1}) j + (z_{2} - z_{1}) k

To given question

$U = \vec{P 1 P 2} U = (- 2 - 1) i + (3 - 2) j + (4 - 0) k U = - 3 i + j + 4 k l i k e t h a t v = - i - 4 j + 3 k$

Step2. Calculation of cross product

We know that to find the area of a parallelogram by two vectors. it's necessary to find an orthogonal vector, for that

$u \times v = |\begin{matrix} i & j & k \\ - 3 & 1 & 4 \\ - 1 & - 4 & 3 \end{matrix}| u \times v = [i |\begin{matrix} 1 & 4 \\ - 4 & 3 \end{matrix}| + j |\begin{matrix} - 3 & 4 \\ - 1 & 3 \end{matrix}| + k |\begin{matrix} - 3 & 1 \\ - 1 & - 4 \end{matrix}|] u \times v = 19 i + 5 j + 13 k$

Step3. Area of parallelogram

$||u \times v|| = |19 i + 5 j + 13 k| ||u \times v|| = \sqrt{361 + 25 + 169} ||u \times v|| = \sqrt{555}$

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In Problem, find the area of the parallelogram with one corner at P1 and adjacent sides
$\vec{P 1 P 2} a n d \vec{P 1 P 3}$
$P 1 = (1, 2, 0), P 2 = (- 2, 3, 4), P 3 = (0, - 2, 3)$

Short Answer

Step by step solution

Step1. Giving information

Step2. Calculation of cross product

Step3. Area of parallelogram

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In Problem, find the area of the parallelogram with one corner at P1 and adjacent sides P1P2→andP1P3→P1=1,2,0,P2=-2,3,4,P3=0,-2,3

Short Answer

Step by step solution

Step1. Giving information

Step2. Calculation of cross product

Step3. Area of parallelogram

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Decision Maths

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Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

In Problem, find the area of the parallelogram with one corner at P1 and adjacent sides
$\vec{P 1 P 2} a n d \vec{P 1 P 3}$
$P 1 = (1, 2, 0), P 2 = (- 2, 3, 4), P 3 = (0, - 2, 3)$