Question

Given that A+B=C. If |A| = |B| = 10 and C = 10√(2+√3). Find the angle between A and B.

(A) 30 degree
(B) 45 degree
(C) 60 degree
(D) 90 degree

Answer 1

Answer:

30°

Explanation:

Magnitude of addition of two vectors A and B seperated by angle ∅ is given as

• |A + B| = √(A² + B² + 2ABCos∅)

It's given that A + B = C which means |A + B| = |C|

So,

10√(2 + √3) = √[10² + 10² + (2 × 10 × 10 × Cos∅)]

10√(2 + √3) = √[200 + 200Cos∅]

Squarring on both sides

100(2 + √3) = 200(1 + Cos∅)

Divide both sides by 100

2 + √3 = 2(1 + Cos∅)

2 + √3 = 2 + 2Cos∅

√3 = 2Cos∅

Cos∅ = √3/2

Cos∅ = Cos30°

∅ = 30°