fund th andle behmaes netos A=3-89 and B=-4ARS3↑-89 and B=-44-123Micheel Roger

The dot product of two vectors is given by A→·B→=A→B→ cosθ Here, θ is an angle between two vectors.…

Answered: fund the andle boetimoes neitos A=3↑-89…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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fund th andle behmaes netos A=3-89 and B=-4ARS
3↑-89 and B=-44-123
Micheel Roger

Expert Solution

Step 1

The dot product of two vectors is given by

$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos θ$

Here, $θ$ is an angle between two vectors.

Given data:

Vector, $\vec{A} = 3 \hat{i} - 8 \hat{j}$

Vector, $\vec{B} = - 4 \hat{i} - 12 \hat{j}$

Here, $A_{1} = 3$ , $B_{1} = - 4$ , $A_{2} = - 8$ , $B_{2} = - 12$

And the magnitude $\begin{array}{rcl} |\vec{A}| \end{array}$ and $\begin{array}{rcl} |\vec{B}| \end{array}$ is given by

$\begin{array}{rcl} |\vec{A}| & = & \sqrt{{(3)}^{2} + {(- 8)}^{2}} \\ = & 8.54 \end{array}$

$\begin{array}{rcl} |\vec{B}| & = & \sqrt{{(- 4)}^{2} + {(- 12)}^{2}} \\ = & 12.64 \end{array}$

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