Evaluate the dot product $\vec{A} \cdot \vec{B}$ if $\vec{A} = 9\hat{i} + 3\hat{j}$ and $\vec{B} = 5\hat{i} - 5\hat{j}$.**Equation Area:**\[\vec{A} \cdot \vec{B} = \]**Explanation:**To calculate the dot product of two vectors $\vec{A}$ and $\vec{B}$, use the formula:\[\vec{A} \cdot \vec{B} = (A_x \times B_x) + (A_y \times B_y)\]Where:- $\vec{A} = 9\hat{i} + 3\hat{j}$ has components $A_x = 9$ and $A_y = 3$.- $\vec{B} = 5\hat{i} - 5\hat{j}$ has components $B_x = 5$ and $B_y = -5$.Calculate:\[\vec{A} \cdot \vec{B} = (9 \times 5) + (3 \times -5) = 45 - 15 = 30\]Therefore, $\vec{A} \cdot \vec{B} = 30$. The task is to evaluate the dot product $\vec{A} \cdot \vec{B}$ given that $\vec{A} = 9\hat{i} - 5\hat{j}$ and $\vec{B} = 5\hat{i} + 3\hat{j}$.The interface includes options for formatting mathematical expressions, such as inserting square roots or Greek letters, along with the reset, undo, and help buttons. There is a text box for typing the solution to the dot product calculation.To calculate the dot product:\[\vec{A} \cdot \vec{B} = (9\hat{i} - 5\hat{j}) \cdot (5\hat{i} + 3\hat{j})\]This can be expanded to:\[= (9 \times 5) + (-5 \times 3)\]\[= 45 - 15\]\[= 30\]Thus, $\vec{A} \cdot \vec{B} = 30$.

Concept of dot product, Consider, vector A = Ax î + Ay ĵ + Az k̂ Vector B = Bx î + By ĵ + Bz k̂ In…

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Evaluate the dot product A · B if A = 92 +3ĵ and B = 5i – 5j. - ? A.B =

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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