Q. 44 Create an application different ... [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. 44 (page 613)

Create an application different from any found in the text that requires a dot product.

Short Answer

Expert verified

We can prove the law of cosines using dot product.

$a^{2} = b^{2} + c^{2} - 2 b c \cos 伪 b^{2} = a^{2} + c^{2} - 2 a c \cos 尾 c^{2} = a^{2} + b^{2} - 2 a b \cos 纬$

Step by step solution

Step 1. An application that requires a dot product.

We can prove the law of cosines using dot product.

$a^{2} = b^{2} + c^{2} - 2 b c \cos 伪 b^{2} = a^{2} + c^{2} - 2 a c \cos 尾 c^{2} = a^{2} + b^{2} - 2 a b \cos 纬$

Step 2. Proving the law of cosines using dot product.

Let three vectors represent the sides of the triangle.

Let

$||\overset{鈫�}{a}|| = a ||\overset{鈫�}{b}|| = b ||\overset{鈫�}{c}|| = c$

Let angle is $伪$ between the $\overset{鈫�}{b}$ and $\overset{鈫�}{c}$ .

Apply triangle law of vector addition,

$\overset{鈫�}{a} = \overset{鈫�}{b} + \overset{鈫�}{c} \overset{鈫�}{a} 路 \overset{鈫�}{a} = (\overset{鈫�}{b} + \overset{鈫�}{c}) 路 (\overset{鈫�}{b} + \overset{鈫�}{c}) a^{2} = \overset{鈫�}{b} 路 \overset{鈫�}{b} + \overset{鈫�}{b} 路 \overset{鈫�}{c} + \overset{鈫�}{c} 路 \overset{鈫�}{b} + \overset{鈫�}{c} 路 \overset{鈫�}{c} a^{2} = b^{2} + c^{2} + 2 \overset{鈫�}{b} 路 \overset{鈫�}{c} a^{2} = b^{2} + c^{2} + 2 ||\overset{鈫�}{b}|| ||\overset{鈫�}{c}|| \cos 伪 a^{2} = b^{2} + c^{2} + 2 b c \cos 伪$

Similarly we can prove

$b^{2} = a^{2} + c^{2} - 2 a c \cos 尾 c^{2} = a^{2} + b^{2} - 2 a b \cos 纬$

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91影视

Create an application different from any found in the text that requires a dot product.

Short Answer

Step by step solution

Step 1. An application that requires a dot product.

Step 2. Proving the law of cosines using dot product.

One App. One Place for Learning.

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