Question

13. If vectors A, B and C have magnitudes 8, 15 and 17
units and A + B = C, find the angle between A and
B.
​

Answer 1

Answer:

Let θ be the angles between the vectors a and b.

Magnitude of the Vector a = 8 units.

Magnitude of the Vectors b = 15 units.

Magnitude of the Vectors c = 17 units.

Now, The magnitudes of a, b and c can be written as ⇒

|a|² + |b|² + |a||b| Cos θ = |c|²

∴ |8|² + |15|² + |8||15| Cos θ = |17|²

⇒ 64 + 225 + 120 Cos θ = 289

⇒ 289 + 120 Cos θ = 289

⇒ 120 Cos θ = 289 - 289

⇒ 120 Cos θ = 0

∴ Cos θ = 0/120

∴ Cos θ = 0

⇒ Cos θ = Cos 90°

On comparing,

θ = 90°