Given |a|=10, |b|=15, and |a+b|=20, find |a-b|
2 answers
This question is about vector.
Draw the parallelogram with sides a and b, where the angle from a to be is θ. Then |a+b| is the length of one diagonal
|a+b|^2 = a^2 + b^2 + 2ab cosθ
plug in your numbers, and you can see that cosθ = 1/4
The length of the other diagonal is
|a-b|^2 = a^2 + b^2 - 2ab cosθ = 250
so |a-b| = 5√10
|a+b|^2 = a^2 + b^2 + 2ab cosθ
plug in your numbers, and you can see that cosθ = 1/4
The length of the other diagonal is
|a-b|^2 = a^2 + b^2 - 2ab cosθ = 250
so |a-b| = 5√10
1 answer