Given vectors u ⃗ u ⃗ u ⃗ and v ⃗ v ⃗ v ⃗ , sketch the resultant vector u ⃗ − v ⃗ u ⃗-v ⃗ u ⃗ − v ⃗ .

In this problem, we are given vectors u and v, and we are asked to sketch the resultant vector u minus v. Now, to solve this, notice we have a subtraction of 2 vectors, and subtracting vectors can also be written as adding negative vectors. So u minus v could also be written as u plus negative v. Now the reason I'm writing it like this is because this actually allows us to deal with the graph we have over here and switch around these vectors. Now I'm going to start by figuring out what negative v is. Well, we see that vector v looks like that and to find negative v, negative v is just going to point in the opposite direction of v, but have the same magnitude. So we can take this and draw it so it's pointing in the opposite direction notice it's the same length, but now it's pointing to the left instead of the right. So now that we have vector negative v, I can use the tip to tail method to add a u and negative v. So we can see we have vector u that's drawn for us, then what I'm going to do is connect the tip of vector u to the tail of vector negative v, And from here, all I need to do is connect these vectors with the resultant vector by taking the initial point of the first vector and connecting it to the terminal point of the last vector, and that will give us the resultant vector u minus v. Now this vector here, this vector can be drawn anywhere on this grid here. So we could draw it there, or we could draw it over here or right there. It doesn't matter where the vector is drawn. All that matters is that it has the correct magnitude and direction that we have right there. So hope you found this video helpful. That's the solution to the problem. Thanks for watching.

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14. Vectors

Geometric Vectors

Precalculus

14. Vectors

Geometric Vectors

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Multiple Choice

Given vectors $u ⃗$ and $v ⃗$ , sketch the resultant vector $u ⃗-v ⃗$ .

option a

option b

option c

option d

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Verified step by step guidance

Identify the given vectors u⃗ and v⃗ in the image. Vector u⃗ is pointing upwards, and vector v⃗ is pointing to the right.

To find the resultant vector u⃗ - v⃗, you need to reverse the direction of vector v⃗ to get -v⃗. This means vector -v⃗ will point to the left.

Place the tail of vector -v⃗ at the head of vector u⃗. This is because subtracting vectors involves adding the negative of the second vector.

Draw the resultant vector from the tail of u⃗ to the head of -v⃗. This new vector represents u⃗ - v⃗.

Ensure the resultant vector is correctly drawn by checking that it forms a triangle with the original vectors u⃗ and -v⃗, following the vector addition/subtraction rules.