   Chapter 12.3, Problem 24E

Chapter
Section
Textbook Problem

# Determine whether the given vectors are orthogonal, parallel, or neither.24. (a) u = ⟨−5, 4, −2⟩ v = ⟨3, 4, −1⟩(b) u = 9i − 6j + 3k, v = −6i + 4j −2k(c) u = ⟨c, c, c⟩, v = ⟨c, 0, −c⟩

(a)

To determine

Whether the vectors are orthogonal, parallel, or neither.

Explanation

Given:

u=5,4,2 and v=3,4,1 .

Formula:

A minimum of two vectors are required to form a dot product. The resultant dot product of two vectors is scalar. So, the dot product is also known as a scalar product

Consider a general expression to find the dot product between two three-dimensional vectors.

uv=a1,a2,a3b1,b2,b3

uv=a1b1+a2b2+a3b3 (1)

Condition for orthogonal:

Two vectors u and v are orthogonal if and only if uv=0

(b)

To determine

To find: Whether the vectors are orthogonal, parallel, or neither.

(c)

To determine

To find: Whether the vectors are orthogonal, parallel, or neither.

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