This question is driving me insane!!?

Question

Vector A has magnitude 4.0 units vector B has magnitude 6.0 units. The angle between A and B is 60.0 degrees. What is the magnitude of A + B.

Note: I spent 50 minutes on this freakin problem. Please be detailed with your explations, lol. Thanks :)

Hey, I tried the method below, and I didnt get that answer. Maybe Im doing my calculations wrong. What answer did you get?

Kemmy, do you have AOL, because I totally need your help.

P.S you got it right! :)

Answer 1

1) Draw vector "A" horizontally (c'mon, get your pencil), pointing to the right.
2) Starting at the tip of "A" (right side), draw vector "B". It will point up and to the right, at an angle of 60° from the horizontal.
3) Now draw "C" (i.e. the sum of A and B). This will be a vector that starts at the tail of "A" (on the left) and ends at the head of "B" (on the right).

Now what?

3) Now break "B" into horizontal & vertical components (hint: you'll need cos(60) and sin(60) to do this). Helps if you draw.
4) The horizontal component of "A" plus the horizontal component of "B" equals the horizontal component of "C"
5) The vertical component of "A" (hint: there isn't one) plus the vertical component of "B", equals the vertical component of "C"
6) Now that you know the horizontal & vertical components of "C", use the pythagorean theorem to find the magnitude (length) of C.

Answer 2

Take vector A and move it to the endpoint of vector B the angle of A with the prolongation of B is 60 degrees so the interior angle of the triangle formed by A and B and the sum vector A+B is 120 degrees (exterior angle =60 degrees so interior is equal to 180-60). Use the law of cosines to get |A+B|^2=|A|^2+|B|^2-2|A||B|cos120 wich gives |A+B|=Squareroot(16+36-2x4x6cos120) = Srt(52-48x(-0.5))= Sqrt(52+24)=Sqrt(76) wich is aproximately 8.7177 units

Answer 3

Total loss of human contact, total seclusion, no access to anything that would stimulate the mind or body, with total deafening silence, and being within a 8x8 room, no way of seeing outside, for months or years. I don't know for a fact that it would drive one insane, but it would definitely have a very serious psychological effect on a person. My own opinion says it would drive one insane.

Answer 4

Use the law of cosines to solve:

a^2 + b^2 - 2ab(cos(angle)) = c^2

Where a is the magnitude of Vector A and b is the magnitude of vector B and the magnitude of A + B is c

Angle is 60 degrees.

Answer 5

Draw out the vector parallelogram.

Cosine rule:
x^2 = 6^2 + 4^2 - (2)(6)(4)cos120
x^2 = 36 + 16 - 48(-0.5)
x^2 = 76
x = 8.72 units (to 3 sig fig)

Answer 6

8.73 and 4.298