Vector addition and subtraction. feeling stupid for being confused over this

In summary, the conversation discusses how to calculate the sum and difference of two vectors A and B, given their Cartesian representations. The options of using angles or directly solving for the answer are considered, and it is suggested to draw the vectors on graph paper to clear up confusion. It is also noted that the two methods will yield the same answer, as long as the angles are correctly accounted for. The problem statement also asks for a vector diagram to be drawn for the calculations.
  • #1

Homework Statement

A = 2i + 3j
B = -5i + 6j

Calculate (draw vector diagram)
A + B
A - B

Homework Equations

actually we're just confused as to whether we need to use the angles to answer this or just answer it directly, meaning that for A + B the answer would be -3i + 9j

The Attempt at a Solution

do we use

A + B = -3i + 9j

or solve for the angles(*rounded off) and use

A+B = ((√13)cos56 + (√61)cos50)i + ((√13)sin56 + (√61)sin50)j

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  • #2
Try drawing the vectors on graph paper, and adding/subtracting head-to-tail.
They are simple enough to do this, and it will clear up your confusion.

The vectors are provided to you in Cartesian representation. If you do it by angles, you want the polar representation. These are entirely equivalent and will get you the same answers. (provided you worked out the angles correctly - yours are all in the 1st quadrant but the vectors are not... one is in the 4th quadrant so it's angle is greater than 270 degrees - I have not checked that you've accounted for this.)
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  • #3
The problem statement asks you to 'draw vector diagram' for A+B and A-B. Did you do that?

1. What is vector addition and subtraction?

Vector addition and subtraction are mathematical operations used to combine or separate vectors, which are quantities that have both magnitude and direction. It is commonly used in physics and engineering to describe the motion and forces acting on objects.

2. How do you add vectors?

To add vectors, you must first make sure they are in the same format, meaning they have the same units and are either both in vector notation (magnitude and direction) or in component form (x and y components). Then, you can simply add the magnitudes of the vectors and use the parallelogram method or the head-to-tail method to determine the direction of the resulting vector.

3. What is the parallelogram method?

The parallelogram method is a graphical method used to add vectors. It involves drawing a parallelogram using the vectors as adjacent sides, and the diagonal of the parallelogram represents the resulting vector. The magnitude and direction of the resulting vector can be determined by measuring the length and angle of the diagonal.

4. How do you subtract vectors?

Subtracting vectors is similar to adding them. Again, make sure they are in the same format and then subtract the magnitudes. However, when using the head-to-tail method, the direction of the second vector must be flipped 180 degrees before adding it to the first vector.

5. What are some real-life applications of vector addition and subtraction?

Vector addition and subtraction are used in a variety of real-life applications, such as navigation systems, flight paths of airplanes, and determining the trajectory of projectiles. They are also used in the fields of physics, engineering, and mathematics to model and analyze various physical phenomena.

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