From number 6 not quite sure part a b and c it said evaluate the following expression if they are allowed mathematically 6) Given the three vectors A = 1.00 î – 4.00 j, B = 3.00 î, and Ĉ = -2.00 ĵ evaluate thefollowing expressions if they are allowed mathematically: (a) C · (Ã + B); (b) C (Ã ·B);(c) C + Ả · B7) Given three vectors, A = 2.00 - 5.00 j, B = 4.00 ĵ, and Ĉ = 3.00 î, evaluate thefollowing expressions if they are mathematically allowed: (a) C(Ã × B); (b) Č · (Ã × B) ;(c) č x (Ä · B)%3D

(6) Given: A→=1 i^-4 j^, B→=3 i^, C→=-2 j^ Required: (a) C→·A→+B→ (b) C→·A→·B→ (c) C+A→·B→ (a)…

Answered: 6) Given the three vectors A = 1.00 î -…

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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From number 6 not quite sure part a b and c it said evaluate the following expression if they are allowed mathematically

6) Given the three vectors A = 1.00 î – 4.00 j, B = 3.00 î, and Ĉ = -2.00 ĵ evaluate the
following expressions if they are allowed mathematically: (a) C · (Ã + B); (b) C (Ã ·B);
(c) C + Ả · B
7) Given three vectors, A = 2.00 - 5.00 j, B = 4.00 ĵ, and Ĉ = 3.00 î, evaluate the
following expressions if they are mathematically allowed: (a) C(Ã × B); (b) Č · (Ã × B) ;
(c) č x (Ä · B)
%3D

Expert Solution

Concept:

(6) Given: $\vec{A} = 1 \hat{i} - 4 \hat{j}, \vec{B} = 3 \hat{i}, \vec{C} = - 2 \hat{j}$

Required: (a) $\vec{C} \cdot (\vec{A} + \vec{B})$ (b) $\vec{C} \cdot (\vec{A} \cdot \vec{B})$ (c) $C + (\vec{A} \cdot \vec{B})$

(a) $\vec{A} + \vec{B} = (1 \hat{i} - 4 \hat{j}) + (3 \hat{i}) = 4 \hat{i} - 4 \hat{j}$

$\vec{C} \cdot (\vec{A} + \vec{B}) = (- 2 \hat{j}) (4 \hat{i} - 4 \hat{j}) = 8$ , $(S i n c e \hat{j} \cdot \hat{i} = 0 a n d \hat{j} \cdot \hat{j} = 1)$

(b) $\vec{A} \cdot \vec{B} = (1 \hat{i} - 4 \hat{j}) (3 \hat{i}) = 3$ , $(S i n c e \hat{j} \cdot \hat{i} = 0 a n d \hat{i} \cdot \hat{i} = 1)$

Since, $\vec{A} \cdot \vec{B}$ is a scalar the dot product of $\vec{C}$ with $\vec{A} \cdot \vec{B}$ is not possible.

From part (b) $\vec{A} \cdot \vec{B} = 3$ , so $C + (\vec{A} \cdot \vec{B}) = 2 + 3 = 5$ .

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