Calculating Vector Quantity with Given Magnitude and Direction

[Physicsnoob90]

Homework Statement

Vector A has magnitude A = 4.0 units and is directed θA = 15◦ counterclockwise from the positive x-axis. Vector B has magnitude B = 4.0 units and is directed θB = 85◦ counterclockwise from the positive x-axis. Determine the following quantity: |A + B|^2 − |A − B|^2.

Homework Equations

The Attempt at a Solution

Steps) 1. i calculated their components: Ax= 4.0 cos 15º = 3.86, Ay= 4.0 sin 15º = 1.04 , A= 4.898979486
Bx= 4.0 cos 85º = 0.35 , By= 4.0 sin 85º = 3.98 , B= 4.333401763

2. plug into the format: |(4.898979486)^2 + (4.333401763)^2| - |(4.898979486)^2 - (4.333401763)^2| = 38

 

[jedishrfu]

Look at the A+B and A-B terms in your expression are they vectors or scalars?

 

[Physicsnoob90]

they are vectors

 

[jedishrfu]

So what you wrote added the lengths of the components of A and B together which is not right.

when instead you should find the length of the new vector A+B and square it for your expression.

 

[Physicsnoob90]

i thought it was asking to add the components of the vector A and B while also figuring out the quantity |A+B|^2 - |A-B|^2?

 

[jedishrfu]

The notation |A+B| means the length of the vector A+B just as |A| means the length of The vector A.

 

[Physicsnoob90]

So would creating a new vector like vector C = A+B?

 

[jedishrfu]

Yes and then find the length of C to use in your expression similarly for the |A-B| term which is the length of the vector A-B.

Have you drawn these four vectors on paper? The A and B represent the sides of a parallelogram and the A+B is one diagonal.

Do you know what the other vector is?

 

[Physicsnoob90]

isn't the other vector the opposite diagonal to A+B?

 

[jedishrfu]

Yes it is.

Did you figure out the answer now?