Refer to vectors a through h...

Question

Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.

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a + (b + c)

a + (b + c)

Accepted Answer

Hey, everyone here, we are asked to refer to the vectors shown below and sketch the vector. As indicated, we need to use the parallelogram rule to get the resultant. We are given our three vectors PQ and R and we need to find P plus the quantity of Q plus R. We have four answer choice options, answer choices A through D, each of which show different variations of our three given vectors as well as the resultants. So to begin finding our overall resultant of P plus the quantity of Q plus R, we want to begin by finding just Q plus R. So we first need to sketch our two vectors Q and R. So starting with Q, we have a small arrow pointed slightly upward. And again, we label this as Q accordingly. Next, we sketch R as another arrow starting from the tail of Q and going slightly upwards but still below Q. And we label this arrow as R. Now we know that the resultant is in between our two vectors. So we just need to draw a third arrow directly in between our Q and R vectors. And this is the resultant vector Q plus R. Now we just want to complete the parallelogram by connecting each head of each arrow by a dash line. And now that we have found Q plus R, we want to continue adding to this current sketch. So we find our full final results in. So our next step here is to sketch in our P vector by just starting again where all of the tails of each arrow meet. And so we draw an arrow from the tail of the other arrows and it points slightly upward. And we label this arrow as P. Now, we can notice that Q sits directly in the middle of the vector P and the vector Q plus R. So the resultant vector of P and Q plus R is laying on top of the Q vector. So we have another arrow that we want to draw in, in between our P vector and the Q plus R vector. And this is the resulting vector P plus the quantity of Q plus R. And now we just want to finish the parallelogram by once again connecting each head of each arrow by a dashed line. And with this final drawing, we have used the parallelogram rule to get our final vector of P plus the quantity of Q plus R. And with this final sketch, we are left with answer choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Key Concepts

Vector Addition

Parallelogram Rule

Associative Property of Vector Addition

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