Chapter 9: Q. 19 (page 627)

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

Short Answer

Expert verified

v ×w= -i +2j +2k

w ×v= i -2j -2k

w ×w=0

v ×v=0

Step by step solution

Step 1. Given Information

v = 2i - j + 2k

w = j - k

Step 2. Cross product v× w

For two vectors

v=a₁i+b₁j+c₁k

w=a₂i+b₂j+c₂k

cross product v× w is written as

v = 2i - j + 2k

w = j - k

$v \times w = |\begin{matrix} i & j & k \\ 2 & - 1 & 2 \\ 0 & 1 & - 1 \end{matrix}| = i |\begin{matrix} - 1 & 2 \\ 1 & - 1 \end{matrix}| - j |\begin{matrix} 2 & 2 \\ 0 & - 1 \end{matrix}| + k |\begin{matrix} 2 & - 1 \\ 0 & 1 \end{matrix}| = - i + 2 j + 2 k$

Step 3. w × v

According to the algebraic properties of cross product

w × v = -(v × w)

so w × v= $-$ (-i+2j+2k) = i -2j -2k

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 ×a=0).

Hence w ×w=0 and v ×v=0

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Cross product v× w

Step 3. w × v

Step 4. w× w and v× v

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Cross product 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

Geometry

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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