Trace the vectors in FIGURE EX3.1 onto your paper. Then find A → − B → \overrightarrow{A}-\overrightarrow{B} .

Hey, everyone in this problem given the vectors A and B, we're asked to find A minus B following the rules of vector addition. Now we're given the vector B in green and that's a vector that points up to the right and we're giving the vector A in red, it points up to the left. OK. A is a longer vector. It's a little bit steeper slope as well. So what we wanna do is we want to find A minus B. Now recall that we can write this as a plus negative beef. OK. So we can use our rules of vector addition because we can write this as an addition of the vector A with the vector negative B. Mhm. So let's start by drawing what negative B looks like. OK. Remember to negate B, we're going to switch the direction. OK. So if we have negative B instead of it pointing upwards into the right, it's gonna be the same magnitude, it's gonna have the same slope, but it's gonna point down to the left. OK. And this is gonna be minus B negative B. So now we have our vector A and we're gonna add it to our vector negative B OK. And remember to add vectors, we add them tip to tip. So what do I mean by that? Well, we're gonna take vector A and I'm gonna draw vector A as best as I can. We have this longer vector, the fairly steep slope pointing up to the left. This is a into the tip of A. We're gonna add the tail of the vector we're adding, which is negative B OK. So the tip of A to the tail of negative B, we draw that vector negative B and the resulting vector is gonna be the vector that joins. Now the tail of A to the tip of B OK. It's gonna join and complete that triangle. OK? We have two sides of a triangle and the resulting vector is going to complete the triangle. And so that resulting vector we're gonna draw in blue is pointing up to the left. It's not a very steep slope and that vector is A minus B. So that is the resulting vector when we take A minus B. Thanks everyone for watching. I hope this video helped see you in the next one.

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3. Vectors

Introduction to Vectors

Physics

3. Vectors

Introduction to Vectors

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Problem 2b

Textbook Question

Trace the vectors in FIGURE EX3.1 onto your paper. Then find $\vec{A} - \vec{B}$ .

Verified step by step guidance

Step 1: Understand the problem. You are tasked with finding the vector subtraction A - B. This involves reversing the direction of vector B and then adding it to vector A.

Step 2: Reverse the direction of vector B. To subtract vector B from vector A, you need to first reverse the direction of vector B. This means flipping vector B so that it points in the opposite direction while maintaining its magnitude.

Step 3: Place the tail of the reversed vector B at the head of vector A. This is the graphical method of vector addition, where you align the vectors tip-to-tail.

Step 4: Draw the resultant vector. The resultant vector (A - B) is drawn from the tail of vector A to the tip of the reversed vector B.

Step 5: If needed, calculate the magnitude and direction of the resultant vector using trigonometry or the Pythagorean theorem, depending on the given components or angles of vectors A and B.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vector Subtraction

Vector subtraction involves finding the difference between two vectors, A and B, resulting in a new vector, A - B. This is done by reversing the direction of vector B and then adding it to vector A. The resultant vector represents the change in position or direction from the tip of vector B to the tip of vector A.

Vector Representation

Vectors are represented graphically as arrows, where the length indicates the magnitude and the direction indicates the vector's direction. In the context of the question, vectors A and B are shown with specific orientations and lengths, which are crucial for accurately performing vector operations like subtraction.

Graphical Addition of Vectors

Graphical addition of vectors involves placing the tail of one vector at the tip of another to find the resultant vector. This method is essential for visualizing vector operations, such as subtraction, where the vector to be subtracted is inverted and then added to the original vector, allowing for a clear understanding of the resultant direction and magnitude.

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