Chapter 12.3, Problem 24E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Determine whether the given vectors are orthogonal, parallel, or neither.

**24.** (a) **u** = ⟨−5, 4, −2⟩ **v** = ⟨3, 4, −1⟩

(b) **u** = 9**i** − 6**j** + 3**k**, **v** = −6**i** + 4**j** −2**k**

(c)** u** = ⟨*c*, *c*, *c*⟩, **v** = ⟨*c*, 0, −*c*⟩

(a)

To determine

Whether the vectors are orthogonal, parallel, or neither.

Explanation

**Given:**

**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.

**Condition for orthogonal:**

Two vectors

(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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