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Precalculus Mathematics for Calculus

Found in: Page 646

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Dot Products
Find the indicated quantity, assuming that $u = 2 i + j, v = i - 3 j & w = 3 i + 4 j$
$(u \cdot v) (u \cdot w)$

The required value of dot product is $- 10$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Vectors are given as

$\begin{array}{l} u = 2 i + j \\ v = i - 3 j \\ w = 3 i + 4 j \end{array}$

Step 2. Concept used

The dot product of two vectors $u$ and $v$ can be defined as-

$u \cdot v = a_{1} b_{1} + a_{2} b_{2}$

Where $u = (a_{1}, a_{2}) & v = (b_{1}, b_{2})$

Properties of the dot product of vectors

$u \cdot u = | u |^{2}$

Transform the required expression and find the value using the dot product of vectors.

Step 3. Calculation

Using Properties of the dot product of vectors,

$\begin{array}{l} (u \cdot v) (u \cdot w) = [(2) (1) + (1) (- 3)] \times [(2) (3) + (1) (4)] \\ = (2 - 3) \times (6 + 4) \\ = (- 1) \times (10) \\ = - 10 \end{array}$

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