Question

If the magnitude of the vectors A, B and C are 6,8,10 units respectively and if A+B=C, then the angle between A and C is

Answer 1

Angle will be cos inverse 3/5.Hope it helps

Answer 2

Given:

A = 6

B = 8

C = 10

A+B=C

To Find:

the angle between A  and C

Solution:

we have,

A+B=C

B=C-A

Squaring both sides

B² = C² + A² - 2CA cosФ

8² = 10² + 6² - 2 (10) (6) cosФ

64 = 100 + 36 - 120 cosФ

64 - 136  = -120 cosФ

72 = 120 cosФ

cosФ = 72 / 120 = 3 / 5

Ф = cos⁻¹ (3/5)

So, the angle between A and C = cos⁻¹ (3/5).