Question

Find the angle between two vectors, 10 and 15 units long, when their resultant is (a) 20 units long and (b) 12 units long. Draw the appropriate figure?

Answer 1

`"please see the solution below."`

Explanation:

`"you can use the cosine theorem to solve this problem."`
`c^2=a^2+b^2+2*a*b*cos theta`
`"where;"`

`a)`

`c=20`
`a=10`
`b=15`
`20^2=10^2+15^2+2*10*15*cos theta`
`400=100+225+300*cos theta`
`400=325+300*cos theta`
`400-325=300*cos theta`
`75=300*cos theta`
`cos theta=75/300=1/4`
`theta =75.52 " deg"`

`b)`

`a=10`
`b=15`
`c=12`

`12^2=10^2+15^2+2*10*15*cos theta`
`144=100+225+300*cos theta`
`144=325+300*cos theta`
`144-325=300*cos theta`
`-181=300*cos theta`

`cos theta=-181/300`

`theta=127.11`