For each pair of vectors u and v

Question

For each pair of vectors u and v with angle θ between them, sketch the resultant.

|u| = 12, |v| = 20, θ = 27°

Accepted Answer

Hey, everyone here, we are asked to draw the resultant vector for the pair of vectors with angle alpha between them. Using the given information. Here we are given the absolute value of A is equal to seven. The absolute value of B is equal to 15 alpha is equal to 54 degrees. We have four answer choice options, answer choices A through D, each of which shows some drawing of two vectors, the angle between them and the resultant vector. So to begin this problem, we first want to notice that we are given the vectors A and B. So we can begin by drawing our vector A as an arrow pointing slightly upward. And we just label this arrow as the given value of seven. And now we want to draw in our second vector B by first noticing that the angle between our two vectors is 54 degrees. So we draw our second vector as an arrow pointing slightly downward. And we know that the angle in between our two arrows is the given angle 54 degrees. So we can go ahead and label that angle. And now with our second vector, we want to notice that its tail connects to the tail of the first vector. And that this second vector is longer than the first since B is larger than A. So now we just want to label our second vector as the given value for B which is 15. Now our next step is to sketch in our resultant vector. So we just draw an arrow in between our two vectors, we have sketched so far. So we have an arrow directly in between our two vectors. And so now we just want to connect each of the heads of each arrow by a dash line so that we finish our parallelogram. And with this, we have finished our drawing of the resultant vector and our given information. And with this, we are left with answer choice C where again, we have our two vectors drawn as seven and 15, the angle between them is 54 degrees. And we also included our resultant vector. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

For each pair of vectors u and v with angle θ between them, sketch the resultant.

|u| = 12, |v| = 20, θ = 27°

Key Concepts

Vector Addition

Magnitude of a Vector

Angle Between Vectors

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