Question

If A and B are two vectors such that |A| = 4 , |B| = ½ and A.B = -1 , the angle between A and B is …..

Answer 1

Explanation:

Formula for calculating the scalar and vector products between two vectors: 

a.b=abcosϕ

∣a×b∣=absinϕ

(a) Given that a=∣a∣=10,b=∣b∣=6.0 and ϕ=600 the scalar (dot) product of a and b is 

a.b = abcosϕ = (10)(6.0)cos600=30

(b) similarly ,  the magnitude of the vector (cross) product of the two vectors is

∣a×b∣ = absinϕ  = (10)(6.0)sin600=52

When two vectors are parallel  (ϕ=0),a.b  = abcosϕ=ab, and ∣a×b∣  =absinϕ=0 .

On the other hand, when the vectors are perpendicular  (ϕ=900),a.b = abcosϕ=0 and ∣a×