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Vector $A$ has components $A_{x}=1.30 \mathrm{cm}, \quad A_{y}=$ $2.25 \mathrm{cm} ; \quad$ vector $\vec{B}$ has components $B_{x}=4.10 \mathrm{cm}$ $B_{y}=-3.75 \mathrm{cm} .$ Find $(\mathrm{a})$ the components of the vector sum $A+B ;$ (b) the magnitude and direction of $\vec{A}+\vec{B}$ (c) the components of the vector difference $\vec{B}-\vec{A}$ (d) the magnitude and direction of $\vec{\boldsymbol{B}}-\vec{\boldsymbol{A}}$

A) $-1.5$B) $344.5^{\circ}$C) $-6$D) $295^{\circ}$

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

McMaster University

Lectures

04:16

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09:56

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Vector $\vec{A}$ has compo…

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14:15

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06:40

Vector $\vec{A}$ has a mag…

07:55

For the vectors $\overrigh…

10:53

Vector $\mathbf{A}$ is 3.0…

04:26

Vector $\overrightarrow{\m…

02:11

06:57

In each of these, the $x$ …

13:05

02:25

The vector $-5.2 \overrigh…

06:12

(a) Write cach vector in F…

05:23

A vector $\overrightarrow{…

01:34

A vector has a magnitude o…

08:42

Vector $\vec{A}$ is 2.80 $…

01:31

The magnitude of vector $\…

03:28

Okay, so we're in Chapter one problem or so this says factor is components. Exp equals one point three centimeters. It has an a Y of 2.25 years. Okay. And we have a B vector with the X equals four point once in years, and B why he calls negative 3.7. Okay, so they asked us to find the components of the vector sum A plus B. Okay, so for a you were a puss. So when we're finding this, we're adding vector components weaken vector. We add the components to each other. So this is same as was called this the result in factor. So now we know that our X equals X plus be packs and our why equals a y plus B y. So if we're looking for the component of the result in factor, that is just the components our ass equals, at least in a very exposed PX is five foot four said amuse in R Y, at least together is negative. 1.5 in the videos. Cool with me. So for being asked us to find the magnitude in direction of Naples. So for a plus B, we always called. We already called This are right. So the magnitude of our is wary of ours. Components so squared. So this most 1.5 squared and you played letting your calculator that should come down to 5.6 centimeters. Cool now for the angle. Let's think about this here. So if our our X is a positive when our allies native that puts our vector here. So when we're looking for the direction we want on that so in that case, this is our father. So this is going to be 270 degrees plus the angle from this small right triangle. And to get that we take the Ark attentions of the opposite. And in this case, that's X value. Our axe 5.4 over the other one. Just 145 We plugged that all on your calculator. You can see that this should come out to being exactly 344. 45 degrees. Cool. Okay, let's move on to see getting change here. See says we want to find the components of the different specter B minus a. So be minus a day equal so called this are now So our X equals Deepak slice a X and B X is 4.1 minus 1.3. So that should give us They resulted of two continents. And the means are why we take bees of negative report 75 and subtract two pulled to five. We should see. This is negative 6.0, Senator. Okay. And for D, Now we got to find the magnet to you of our of our. In this case, this is 2.8 with that person square plus six squared and and see that the magnitude of this comes out needs 6.62 centimeters. Again, let's draw this. We have a positive X value in the negative. Why are the only vectors till down here? Right? Which means we have to do the same path as before. So there are five. A tingle is going to be 2 70 plus mark changes 2.8 over six. Since our X value is the opposite here. So when you put this in, your calculator should see that that comes out to be 295 degrees. Cool. We got it.

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