Chapter 9: Q. 46 (page 630)

In Problems 46–49, find the dot product $v \cdot w$ and the angle between v and w.
$v = - 2 i + j, w = 4 i - 3 j$

Short Answer

Expert verified

The dot product $v \cdot w$ is $- 11$ and the angle betweenv andwis $θ \approx 169 ° .$

Step by step solution

Step 1. Given Information

The given vectors are $v = - 2 i + j, w = 4 i - 3 j .$

Step 2. Finding the dot product

To find the dot product, use the formula of the dot product which is $v \cdot w = a_{1} a_{2} + b_{1} b_{2}$

So,

$v \cdot w = (- 2) (4) + (1) (- 3) v \cdot w = - 11$

Step 3. Finding the angle between v and w

To find the angle between vectors, we will use the formula $\cos θ = \frac{u \cdot v}{||u|| ||v||} .$

We have the dot product but to find the length of a vector we will use $||u|| = \sqrt{a^{2} + b^{2}}$ .

So,

$\cos θ = \frac{(- 2 i + j) \cdot (4 i - 3 j)}{(\sqrt{{(- 2)}^{2} + 1^{2}}) (\sqrt{{(4)}^{2} + {(- 3)}^{2}})} \cos θ = \frac{- 11}{5 \sqrt{5}} θ = \cos^{- 1} (\frac{- 11}{5 \sqrt{5}}) θ \approx 169 °$

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In Problems 46–49, find the dot product $v \cdot w$ and the angle between v and w.
$v = - 2 i + j, w = 4 i - 3 j$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the dot product

Step 3. Finding the angle between v and w

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In Problems 46–49, find the dot product v·w and the angle between v and w.v=-2i+j,w=4i-3j

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the dot product

Step 3. Finding the angle between v and w

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Decision Maths

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In Problems 46–49, find the dot product $v \cdot w$ and the angle between v and w.
$v = - 2 i + j, w = 4 i - 3 j$