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$$\begin{array}{l}{\text { (II) Figure } 36 \text { shows two vectors, } \vec{\mathbf{A}} \text { and } \vec{\mathbf{B}}, \text { whose magni- }} \\ {\text { tudes are } A=6.8 \text { units and } B=5.5 \text { units. Determine } \vec{\mathbf{C}} \text { if }}\end{array} $$ $$ \begin{array}{l}{\text { (a) } \mathbf{C}=\mathbf{A}+\mathbf{B},(b) \mathbf{C}=\mathbf{A}-\mathbf{B},(c) \mathbf{C}=\mathbf{B}-\mathbf{A} \text { . Give the }} \\ {\text { magnitude and direction for cach. }}\end{array} $$

(a) Magnitude: 1.3 units, direction: $+x$(b) Magnitude: 12.3 units, direction: $+x$(c) Magnitude: 12.3 units, direction: $-x$

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Simon Fraser University

Hope College

University of Winnipeg

McMaster University

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our question, says Figure. 36 shows to vectors Vector, AM B. Who's magnitudes are a equals 6.8 units and B equals 5.5 units. Determined. See if sees if a sea is equal to a plus, B, B C is equal to a minus. B and C C is equal to B minus a. Give the magnitude and direction for each of the situations. So I redrew Figure 36 which shows the X and Y coordinate system and shows vector a going in the positive ex direction in Vector be going in the negative extraction along the X axis. So I wrote down here that Vector A is equal to 6.8 units, which I write as you in the positive X hat direction since it's moving. Since the hat represents directionality of a coordinate system, then B is equal to 5.5 units, but it's in the minus X hat direction. Okay, so then the question is what is C equal for the following situations? And I wrote the situations we were given in red, going to go ahead and do the calculations and black okay, So if C is equal to eight plus B. Well, right now what we have for a 6.8 units, right? And that's in the positive x had direction plus and then be well, we can pull that negative sign out front. Okay? From the negative, X had direction, and that is equal to 5.5 units. And since we pulled the negative sign out front, we just write this as X hat. Okay, well, 6.8 you plus negative 5.5. You weaken Adam together, since they're both annex that direction plus the negatives the same as minus that number. Difference between those two is 1.3 units and direction plus x hat on the positive. Excellent direction. Oxidant, is your solution a part? A part B. We want a minus b. So now? No, we have 6.8 units again for a That's in the plus X had direction, right? And then this time we have a minus. And then we also have another minus sign here cause I had the same thing for because it's minus B 90 minutes. Thanks. Okay, Well minus and minus is the same as Plus, so it's goingto being 6.8 plus 5.5, which gives us 12 0.3. Okay, 12.3 units. And that's in the plus X had direction because it's a positive number. Okay, box it in. Other solution for B, then for sea, we want be minus A will be is minus 5.5 units in the exact direction. Right. And then minus a, which is 6.8 years. Well, I forgot my you up here with the 12.3. So we just write that end units and the exact direction, um, 6.8 units in the X hat direction. Okay, We'll make it. A 5.5 minus 6.8 is going to give us negative 12.3 units in the exact direction. But we can just move that minus sign back over to the directionality of X, and that's going to be 12.3 units. And directionality of this is in the minus. X had direction. Oxygen is your solution. See,

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