Solving Vectors Problems in 3D Space

[Petkovsky]

The vectors are in 3D space:
1. It says:
|Q| = 2 and |P| = 3. Angle between the vectors is 30. Find a = P - 2Q.

-- So for this one, i used the angle formula cos (alpha) = (Q*P) / (|Q| * |P|)
and got QP = 3sqrt(3). However i don't know how to proceed from this point on.

2. |a - b| = 22, |a| = 13 ,| b| = 19. Find |a+b|
With this one i honestly don't know how to start.
Edit:
Ok, i drew quadrilateral, with a and b being the sides, and a+b and a-b the diagonals. I think that i might solve it.

 

[tiny-tim]

Hi Petkovsky!

|Q| = 2 and |P| = 3. Angle between the vectors is 30. Find a = P - 2Q.

Do you mean Find a = |P - 2Q| ?

If so, use |A| =√(A.A)

 

[Petkovsky]

Hi Petkovsky!


Do you mean Find a = |P - 2Q| ?

If so, use |A| =√(A.A)

Sorry, my bad, i have copied it wrong. It says find |a| if a = p-2q.

-Solution:
(p-2q)^2 = p^2 - 4pq + 4q^2 = 9 - 12sqrt(3) + 16 = 25 - 12sqrt(3)
|p-2q| = sqrt(25 - 12sqrt(3)) <= is this correct?