Finding the length of a vector given the magnitudes

Homework Statement

The question is as follows: if |m| = 4, |n| = 3, and the angle θ between m and n is 5pi/6, find the norm of the vector m + 2n.

Homework Equations

Im attempting to use the equation :
cosθ = (m * n)/(|m||n|)

The Attempt at a Solution

I determined using the above formula that the value of m * n is 6√(3), and is either negative using the given 5pi/6 or positive if you use the reference angle of pi/6. I am not entirely sure how to relate that value to the length of m +2n. Would you just multiple |n| by 2 in that formula? which would yield 12√3. Again not sure if I can relate these 2 things, thanks

SammyS
Staff Emeritus
Homework Helper
Gold Member

Homework Statement

The question is as follows: if |m| = 4, |n| = 3, and the angle θ between m and n is 5pi/6, find the norm of the vector m + 2n.

Homework Equations

Im attempting to use the equation :
cosθ = (m * n)/(|m||n|)

The Attempt at a Solution

I determined using the above formula that the value of m * n is 6√(3), and is either negative using the given 5pi/6 or positive if you use the reference angle of pi/6. I am not entirely sure how to relate that value to the length of m +2n. Would you just multiple |n| by 2 in that formula? which would yield 12√3. Again not sure if I can relate these 2 things, thanks
The norm of vector, v is is given by: |v| = √(vv).

So, look at (m + 2n)∙(m + 2n)