Two vectors of equal magnitude of 5 unit have an angle `60^0` between them. Find the magnitude of (a) the sum of the vectors and (b) the difference of the vectors. . .

Explanation

ure shows the construction of the sum
` vecA+vecB` and the differece `vecA-vecB`.
`a vecA+vecB` is the sum to `vecA and vecB`. Both have a magnitude of unit nd the angle between them is `60^0`. Thus, the magnitude of the sum is
`|vecA+vecB|=sqrt(5^2+5^2+2xx5x5cos60^0)`
`=2xx5 cos 30^0=5sqrt 3` unit.
b. ` vecA-vecB` is the sum of `vecA and (-vecB)`. As shown in the ure, angle between `vecA and (-vecB)` is `120^0`. The magnitude of both `vecA and (-vecB)` is 5 unit so,
`|vecA-vecB|=sqrt95^2+5^2+2x5xx5 cos 120^0)`
1 = 2xx cos6060 = 5 unit`.