The angle between u,v is 120 degrees, with norm(u) = 4, norm(v) = 3. I need to calculate norm((u−v)) and norm((u+v)). I used (norm(u)^2+norm(v)^2−2 norm(u) norm(v) cos(x))^2 but still not sure.

Aidyn Crosby

Aidyn Crosby

Answered question

2022-09-07

The angle between u,v is 120 degrees, with | | u | | =4, | | v | | =3
I need to calculate | | ( u v ) | | and | | ( u + v ) | | . I used ( | | u | | 2 + | | v | | 2 2 | | u | |   | | v | | cos ( x ) ) 2 but still not sure.

Answer & Explanation

farbhas3t

farbhas3t

Beginner2022-09-08Added 6 answers

u v = u v cos θ
u v = 12 cos 120 0 = 6
u + v 2 = ( u + v ) ( u + v ) = u 2 + v 2 + 2 ( u v ) = 3 2 + 4 2 + 2 × ( 6 ) = 13
So, u + v = 13
u v 2 = ( u v ) ( u v ) = u 2 + v 2 2 ( u v ) = 3 2 + 4 2 2 × ( 6 ) = 37
So, u v = 37

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