Chapter 9: Q. 46 (page 559)

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

Short Answer

Expert verified

The area of the parallelogram is $\sqrt{213}$

Step by step solution

Step1. Given equation

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

We know that the vector is formed by two points like

To given question

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

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

$u \times v = |\begin{matrix} i & j & k \\ 2 & 3 & 1 \\ - 2 & 4 & 1 \end{matrix}| u \times v = [i |\begin{matrix} 3 & 2 \\ 4 & 2 \end{matrix}| + j |\begin{matrix} 2 & 1 \\ - 2 & 1 \end{matrix}| + k |\begin{matrix} 2 & 3 \\ - 2 & 4 \end{matrix}|] u \times v = - i - 4 j + 14 k$

Step3.Calculation of area

The area of parallelogram = $||u \times v||$

$||u \times v|| = |- i - 4 j + 14 k| ||u \times v|| = \sqrt{1 + 16 + 196} ||u \times v|| = \sqrt{213}$

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

Short Answer

Step by step solution

Step1. Given equation

Step2. Calculation of cross product

Step3.Calculation of area

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Applied Mathematics

Geometry

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problem, find the area of the parallelogram with one corner at P1 and adjacent sidesP1P2→andP1P3→P1=0,0,0,P2=2,3,1,P3=-2,4,1

Short Answer

Step by step solution

Step1. Given equation

Step2. Calculation of cross product

Step3.Calculation of area

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Applied Mathematics

Geometry

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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