Question

Find the magnitude of the sum of two vectors; A is 5 km , and B is 7 , when the angle btween them is 120

Answer 1

Answer: 6.24 km

Step-by-step explanation:

Given

The magnitude of the first vector(say)
`\left | a\right |=5\ km`

the magnitude of the second vector(say)
`\left | b\right |=7\ km`

the angle between them is
`120^(\circ)`

The resultant vector magnitude is given by

`\left | \vec{R}\right |=√(a^2+b^2+2ab\cos \theta)`

`\left | \vec{R}\right |=\sqrt{5^2+7^2+2* 5* 7\cdot \cos 120^(\circ)}\\\left | \vec{R}\right |=√(74-35)=√(39)\\\left | \vec{R}\right |=6.24\ km`