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 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.

8. Vectors

Geometric Vectors

Trigonometry

8. 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

Verified step by step guidance

Identify the given vectors $ \vec{u} $ and $ \vec{v} $ from the image. $ \vec{u} $ is a vertical vector pointing upwards, and $ \vec{v} $ is a horizontal vector pointing to the right.

To find the resultant vector $ \vec{u} - \vec{v} $, we need to subtract $ \vec{v} $ from $ \vec{u} $. This is equivalent to adding $ \vec{u} $ and $-\vec{v}$, where $-\vec{v}$ is the vector $ \vec{v} $ reversed in direction.

Draw $-\vec{v}$ by reversing the direction of $ \vec{v} $. Since $ \vec{v} $ points to the right, $-\vec{v}$ will point to the left with the same magnitude.

Place the tail of $-\vec{v}$ at the head of $ \vec{u} $. This is the head-to-tail method of vector addition.

The resultant vector $ \vec{u} - \vec{v} $ is the vector that starts at the tail of $ \vec{u} $ and ends at the head of $-\vec{v}$. Sketch this vector to complete the problem.