# Calculating Angle and Magnitude of Vector Sum A+B+C and -A-B+C | Unit Vectors HW

• chocolatelover
In summary, the angle formed by the vector A+B+C is 90 degrees. The magnitude of the vector -A-B+C is approximately 16.28, and the direction can be found by using inverse tangent, which should yield an angle of approximately 178.9 degrees.
chocolatelover

## Homework Statement

Vector A=(oi +3j), B=(8i-1j), C=(-8i+5j)

Find the angle from the positive x-axis of the vector A+B+C
Find the magnitude and direction of the vector -A-B+C

## The Attempt at a Solution

I know that the answer is 90, but I'm not sure how to get that. I know that theta=tan-1(y/x) and that doesn't equal 90.

As far as the second part, this is what I did:

square root (0-8-8)^2+(-3+1+5)^2 and that supposed to be equal to 16.28, but it's not. Would I use tangent to find the angle?

Could someone please show me how to do this?

Thank you very much

For your first problem, add the three vectors together component by component, and draw the resultant vector. What is y? What is x? What is tan-1(y/x)? Just from the drawing, can you see that the angle is 90 degrees?

For your second problem, you have the right equation, and it does give 16.28. You would use inverse tangent to find the angle.

Thank you very much

Rx=0 and Ry=7(3-1+5), right?

So, x would be 0 and y would 7, right?

For the diagram, would you connect B to C?

For the angle are you just looking at the angle formed by the x-axis and vector A?

Thank you

Well, you are looking for the angle formed by A + B + C, which would be 0i + 7j, as you found.

Thank you very much

Now I see. Could you please show me how to do the second part?

Thank you

You have the right magnitude for the second part; you just must have made an arithmetic error. As for angle, you do have to use inverse tangent, which should be fine since you have i and j of the resultant vector (which you used to find magnitude).

Thank you

Wouldn't it be tan-1(9/264)? but that's 178

## 1. How do you calculate the angle and magnitude of a vector sum?

You can calculate the angle and magnitude of a vector sum by using the Pythagorean theorem and trigonometric functions. First, find the x and y components of each vector. Then, use the Pythagorean theorem to find the magnitude of the sum of the x and y components. Finally, use inverse trigonometric functions to calculate the angle of the sum.

## 2. What is the difference between a vector sum and a vector magnitude?

A vector sum is the result of adding two or more vectors together. It includes both the magnitude and direction of the combined vectors. A vector magnitude, on the other hand, is the size or length of a vector without considering its direction.

## 3. How do you calculate the unit vector of a vector sum?

To calculate the unit vector of a vector sum, divide the sum of the x and y components by the magnitude of the vector sum. The resulting unit vector will have a magnitude of 1 and will point in the same direction as the original vector sum.

## 4. Can you calculate the angle and magnitude of a negative vector sum?

Yes, you can calculate the angle and magnitude of a negative vector sum. The process is the same as calculating a positive vector sum, but you will end up with a negative magnitude and angle.

## 5. What is the importance of calculating the angle and magnitude of a vector sum?

Calculating the angle and magnitude of a vector sum is important in many fields, including engineering, physics, and mathematics. It allows us to understand the relationship between multiple vectors and how they combine to form a resultant vector. This can help in solving problems and making predictions about real-world scenarios.

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