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

[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

Homework Equations

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

 

[Tedjn]

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.

 

[chocolatelover]

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

 

[Tedjn]

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

 

[chocolatelover]

Thank you very much

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

Thank you

 

[Tedjn]

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).

 

[chocolatelover]

Thank you

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