Solving Vector Problems: Vector A, B and C

[chocolatelover]

Homework Statement

Vector A=(0i+3j), vector B=(8i+-1j), vector C=(-8i+5j) Use the component method to determine the following:

1. the magnitude and direction of Vector D=Vector A+vector B+vector C
2. vectorE=-A-B+C

Homework Equations

The Attempt at a Solution

1. magnitude D=A+B+C=square root (0+8+-8)^2+(3+-1+5)^2=9
direction=tan-1(3-1+5/0+8-8) this won't work because I am dividing by zero, but I'm not sure what it would be.

2. Magnitude -A-B+C=square root (-0-8+-8)^2+(-3--1+5)^2=2.65

direction=tan-1(3+-1+5/0+8-8)=undefined

Could someone please show me what I'm doing wrong?

Thank you very much

 

[chocokat]

I did a quick check of your first answer, but it's wrong. You need to recheck your math.

For the i's (0+8-8) = 0
For the j's (3-1+5) = 7

So the magnitude of A+B+C = 7

Now, since the i's represent the x value, and the j's represent the y value, what do you know about the angle that has an x value of 0, and a y value of 7?

 

[chocolatelover]

Thank you very much

Wouldn't the angle just be 90 degrees? Could you show me what I did wrong with the subtraction one?

Thank you

 

[chocokat]

Yes, your angle would just be 90 degrees, or the positive y axis.

For the second problem, I think you're just working too fast.

For the i's (-0-8-8) = -16
For the j's (-3--1+5) = 3

So the magnitude is $$\sqrt{(-16)^2 + 3^2}$$
which equals 16.28

I'm going to let you figure out the angle. Just be careful about where it is, because the i value is negative, and the j value is positive.

 

[chocolatelover]

Thank you very much

Is it tan-1(3+1+5/-0-8-8)=-29.4

180-29.4=150.6?

Thank you

 

[chocokat]

Is it tan-1(3+1+5/-0-8-8)=-29.4

180-29.4=150.6?

Thank you

Not quite, but close. Be careful with the negative signs. The 3 on should be negative, so it's tan-1(3/-16) etc.

 

[chocolatelover]

Thank you very much

Does this look correct?

tan-1(3-1-5/-0-8-8)
=10.62

Do I then need to subtract it from 180?

180-10.62=
169.4

Thank you

 

[chocokat]

Do I then need to subtract it from 180?

180-10.62=
169.4
Thank you

If you want to show the angle from the x axis, then yes, subtract it from 180. And the answer looks good to me.

You're very welcome.

 

[chocolatelover]

Thank you very much again

Regards