Q. 18 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. 18 (page 627)

find (a) v 脳 w, (b) w 脳 v, (c) w 脳 w, and
(d) v 脳 v
v = i - 4j + 2k
w = 3i + 2j + k

Short Answer

Expert verified

v 脳w= -8i +5j +14k

w 脳v= 8i -5j -14k

w 脳w=0

v 脳v=0

Step by step solution

Step 1. Given information

v = i - 4j + 2k

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 = i - 4j + 2k

w = 3i + 2j + k

$v 脳 w = |\begin{matrix} i & j & k \\ 1 & - 4 & 2 \\ 3 & 2 & 1 \end{matrix}| = i |\begin{matrix} - 4 & 2 \\ 2 & 1 \end{matrix}| - j |\begin{matrix} 1 & 2 \\ 3 & 1 \end{matrix}| + k |\begin{matrix} 1 & - 4 \\ 3 & 2 \end{matrix}| = - 8 i + 5 j + 14 k$

Step 3. w × v

According to the algebraic properties of cross product

w 脳 v = -(v 脳 w)

so w 脳 v= $-$ (-8i+5j+14k)= 8i -5j -14k

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

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91影视

find (a) v 脳 w, (b) w 脳 v, (c) w 脳 w, and
(d) v 脳 v
v = i - 4j + 2k
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

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91影视

find (a) v 脳 w, (b) w 脳 v, (c) w 脳 w, and(d) v 脳 vv = i - 4j + 2kw = 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

Pure Maths

Discrete Mathematics

Geometry

Statistics

Mechanics Maths

Applied Mathematics

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 = i - 4j + 2k
w = 3i + 2j + k