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 vectors, i⋅i=j⋅j=k⋅k=1 A · B = (Ax î + Ay ĵ + Az k̂) · (Bx î + By ĵ + Bz k̂) = AxBx + AyBy +AzBz Calculate the value of A.B A.B = (9*5) + (3)(-5) = 45 - 15 = 30 Calculate the value of A.B A.B = (9*5) + (3)(-5) = 45 - 15 = 30

Answered: Evaluate the dot product A · B if A =…

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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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Question

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, \(\vec{A} \cdot \vec{B} = 30\).

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