Find Magnitude & Direction of A+B - Unit Vector Help

In summary, when given two vectors A and B, you can find the magnitude and direction of A + B by adding their components in rectangular coordinates. To find the magnitude and direction in polar coordinates, you need to convert the resultant vector from rectangular to polar coordinates.
  • #1
Loppyfoot
194
0

Homework Statement


Find the magnitude and direction of A + B for the following vectors.

A = -4 i - 1 j, B = 8 i -2 j

How do I find the magnitude of A+B, and also the degree clockwise from the +x direction?
 
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  • #2
Loppyfoot said:

Homework Statement


Find the magnitude and direction of A + B for the following vectors.

A = -4 i - 1 j, B = 8 i -2 j

How do I find the magnitude of A+B, and also the degree clockwise from the +x direction?

You add the components to get the resultant, which is also in rectangular coordinates. Do you know how to convert the resultant vector from rectangular coordinates to polar coordinates (so you can get the resultant magnitude and direction)?
 
  • #3
So would it be 4i - 3j? On my webassign homework, it has to be a single numerical value.
 
  • #4
Loppyfoot said:
So would it be 4i - 3j? On my webassign homework, it has to be a single numerical value.

That's the correct answer in rectangular coordinates. If they are asking for a single number for an answer, did you say they want the angle that the vector forms with some axis? A vector is always made up of 2 numbers (in 2 dimensions). In rectangular coordinates, it's the i and j components. In polar coordinates, it's the magnitude and direction (usually the direction is the angle swinging up from the x-axis to the vector).

Do you know how to convert the vector from rectangular to polar coordinates? That should be in your book.
 
  • #5
Got it. Thanks man!
 

1. What is the formula for finding the magnitude of A+B?

The magnitude of A+B can be found using the Pythagorean theorem, where the square root of the sum of the squares of the individual vector components is taken. In other words, the magnitude is equal to the square root of (A^2 + B^2).

2. How do you find the direction of A+B?

The direction of A+B can be found using trigonometric functions such as sine, cosine, and tangent. First, find the angle between the two vectors using the dot product formula. Then, use inverse trigonometric functions to find the direction in terms of degrees or radians.

3. What is a unit vector?

A unit vector is a vector with a magnitude of 1. It is used to represent the direction of a vector without considering its magnitude. Unit vectors are often represented by the lowercase letter "u" with a vector symbol on top (û).

4. How do you calculate the unit vector of A+B?

To calculate the unit vector of A+B, first find the magnitude of A+B using the Pythagorean theorem. Then, divide each of the individual vector components by the magnitude to get the unit vector in the same direction as A+B.

5. Can you provide an example of finding the magnitude and direction of A+B?

Sure, let's say A = (3, 4) and B = (5, 2). The magnitude of A+B would be √(3^2 + 5^2) = √34. To find the direction, we can use the dot product formula: A ⋅ B = |A| |B| cos θ. Plugging in the values, we get 3(5) + 4(2) = √34 |B| cos θ. Solving for θ, we get cos θ = 3/√34. Using an inverse cosine calculator, we find that θ ≈ 58.63 degrees. Therefore, the direction of A+B is 58.63 degrees from the positive x-axis.

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