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 plus B following the rules of vector edition. Now we're giving the vector B drawn in green and this is a vector that's pointing up into the right. It looks like almost at a 45 degree angle. Then we have vector A drawn in red vector A is a longer vector than vector B. It's pointing up into the left and it is a, it is steeper. OK. So the angle between the horizontal and A is larger than the angle for vector B. So what we wanna do is we wanna add these two vectors A plus B. Now when we wanna add vectors graphically, what we wanna do is we wanna add tip to tell. So when we're talking about the tip of a vector, what we mean is the end with the arrow and the tail is gonna be that opposite bent. OK. So we're gonna take our first vector A, we're gonna draw that out. That's vector A and to the tip of vector A, we wanna add the tail of vector B. So the end with the arrow of A is gonna connect with the end without the arrow of vector B, we're gonna draw B from that point and it looks something like this. OK. So we have vector A vector B and the resulting vector is gonna be the vector that forms a triangle with these two. OK. So vector A is one side of our triangle. Vector B is another side. And if we connect the two to form a triangle, the vector that points from the tail of vector A to the tip of vector B is going to be A plus B. OK. Our resulting vector that we were looking for, that's it for this one. Thanks everyone for watching. I hope this video helped.

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3. Vectors

Introduction to Vectors

Physics

3. Vectors

Introduction to Vectors

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2:13 minutes

Problem 1a

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: Begin by tracing the vectors A and B from the figure onto your paper. Ensure that the directions and magnitudes of the vectors are accurately represented.

Step 2: To find the vector sum A + B, place the tail of vector B at the head of vector A. This is known as the 'tip-to-tail' method for vector addition.

Step 3: Draw a new vector starting from the tail of vector A to the head of vector B. This new vector represents the resultant vector A + B.

Step 4: If the magnitudes and directions of vectors A and B are given, resolve each vector into its components along the x-axis and y-axis. Use the formulas: Ax = |A|cos(θA), Ay = |A|sin(θA), Bx = |B|cos(θB), By = |B|sin(θB), where θA and θB are the angles the vectors make with the positive x-axis.

Step 5: Add the components of the vectors to find the components of the resultant vector: Rx = Ax + Bx, Ry = Ay + By. The magnitude of the resultant vector can be calculated using |R| = √(Rx² + Ry²), and the direction can be found using θR = tan⁻¹(Ry/Rx).

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Key Concepts

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

Vector Addition

Vector addition involves combining two or more vectors to produce a resultant vector. This can be done graphically by placing the tail of one vector at the head of another, or mathematically by adding their components. The resultant vector represents the cumulative effect of the individual vectors in terms of both magnitude and direction.

Vector Components

Vectors can be broken down into their components along the axes of a coordinate system, typically the x and y axes. Each vector can be expressed as a sum of its horizontal (x) and vertical (y) components, which allows for easier calculations in vector addition and other operations. This decomposition is essential for accurately determining the resultant vector.

Graphical Representation of Vectors

Vectors are often represented graphically as arrows, where the length indicates the magnitude and the direction of the arrow indicates the vector's direction. This visual representation helps in understanding vector operations, such as addition and subtraction, and is crucial for solving problems involving multiple vectors, as seen in the question.

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