Q. 15 find (a) v 脳聽w, (b) w 脳聽v, (... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 15 (page 627)

find (a) v $脳$ w, (b) w $脳$ v, (c) w $脳$ w, and
(d) v $脳$ v.
v= 2i - 3j + k
w = 3i - 2j - k

Short Answer

Expert verified

v 脳w= 5i+5j+5k

w 脳v= -5i-5j-5k

w 脳w=0

v 脳v=0

Step by step solution

Step 1. Given information

v= 2i - 3j + k

w = 3i - 2j - k

Step 2. v×w

For two vectors

v=a₁i+b₁j+c₁k

w=a₂i+b₂j+c₂k

cross product v $脳$ w is written as

$v 脳 w = |\begin{matrix} i & j & k \\ a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \end{matrix}| = i |\begin{matrix} b_{1} & c_{1} \\ b_{2} & c_{2} \end{matrix}| - j |\begin{matrix} a_{1} & c_{1} \\ a_{2} & c_{2} \end{matrix}| + k |\begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix}|$

v= 2i - 3j + k

w = 3i - 2j - k

$v 脳 w = |\begin{matrix} i & j & k \\ 2 & - 3 & 1 \\ 3 & - 2 & - 1 \end{matrix}| = i |\begin{matrix} - 3 & 1 \\ - 2 & - 1 \end{matrix}| - j |\begin{matrix} 2 & 1 \\ 3 & - 1 \end{matrix}| + k |\begin{matrix} 2 & - 3 \\ 3 & - 2 \end{matrix}| = 5 i + 5 j + 5 k$

Step 3. w ×v

According to the algebraic properties of cross product w $脳$ v= $-$ (v $脳$ w)

so w $脳$ v= $-$ (5i+5j+5k) =-5i-5j-5k

Step 4. w×w and v×v

According to the algebraic properties of cross product the cross product of any vector with itself is the zero vector

(a 脳a=0).

Hence w 脳w=0 and v 脳v=0

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

find (a) v $脳$ w, (b) w $脳$ v, (c) w $脳$ w, and
(d) v $脳$ v.
v= 2i - 3j + k
w = 3i - 2j - k

Short Answer

Step by step solution

Step 1. Given information

Step 2. v×w

Step 3. w ×v

Step 4. w×w and v×v

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Statistics

Geometry

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

find (a) v 脳w, (b) w 脳v, (c) w 脳w, and(d) v 脳v.v= 2i - 3j + kw = 3i - 2j - k

Short Answer

Step by step solution

Step 1. Given information

Step 2. v×w

Step 3. w ×v

Step 4. w×w and v×v

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Statistics

Geometry

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

find (a) v $脳$ w, (b) w $脳$ v, (c) w $脳$ w, and
(d) v $脳$ v.
v= 2i - 3j + k
w = 3i - 2j - k