Suppose that in the equation F=F_1+F_2+F_3, F=0 N, F_1=8\vec i-3 \vec k N, and F_3=6\vec j+3\vec...


Suppose that in the equation {eq}F=F_1+F_2+F_3, F=0 N, F_1=8\vec i-3 \vec k N, {/eq} and {eq}F_3=6\vec j+3\vec k N. {/eq} The force, {eq}F_2 {/eq} is found in one of the three planes: {eq}xy,yz, {/eq} and {eq}zx {/eq}.

a) Find this plane of {eq}F_2 {/eq}.

b) What is the magnitude of the force {eq}F_2 {/eq}?

Force and vectors

The force is a vector magnitude, so it is characterized by direction and module. In addition, being a vector, mathematically meets all the conditions of vector algebra.

Answer and Explanation:

a) If we consider that {eq}\hat{i} {/eq}, {eq}\hat{j} {/eq} and {eq}\hat{k} {/eq} are the unit vectors in the direction of the X, Y and Z axes respectively, then when calculating the vector value of {eq}\vec{F}_2 {/eq} we will be able to know on which vectors it depends and therefore on which plane it is located.

{eq}\vec{F}=\vec{F}_1+\vec{F}_2+\vec{F}_3=\vec{0}\Rightarrow \vec{F}_2=-(\vec{F}_1+\vec{F}_2)=-(8\hat{i}-3\hat{k}+6\hat{j}+3\hat{k})\,\mathrm{N}=-(8\hat{i}+6\hat{j})\,\mathrm{N} {/eq}

Therefore, force {eq}\vec{F}_2 {/eq} is located in the XY plane.

b) The magnitude of {eq}\vec{F}_2 {/eq} is:

{eq}\vec{F}_2=-(8\hat{i}+6\hat{j})\,\mathrm{N}\Rightarrow F_2=\sqrt{(8\,\mathrm{N})^2+(6\,\mathrm{N})^2}=10\,\mathrm{N} {/eq}

Learn more about this topic:

Practice Adding & Subtracting Vectors

from High School Physics: Homework Help Resource

Chapter 3 / Lesson 23

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