Question

The resultant vector of two other vectors is 10 units long and forms an angle of 35° with one of the component vectors, which is 12 units long. Find the magnitude of the other vector and the angle between the two?

Answer 1

`"the solution is shown below."`

Explanation:

`"resultant c=10 units"`
`"first component a=12 units"`
`"second component b=?"`
`"angle between a and c "alpha=35 " deg"`
`"the triangle method is used in the drawing."`
`vec c=vec a+vec b`
`b^2=a^2+c^2-2*a*c*cos 35`
`cos 35=0.81915204`
`b^2=12^2+10^2-2*12*10*0.81915204`
`b^2=144+100-240*0.81915204`
`b^2=244-196.596`
`b^2=47.404`

`sqrt(b^2)=sqrt(47.404)`
`b=6.89" units"`

`"angle between two components(a,b):"`
`c^2=a^2+b^2+2*a*b*cos beta`

`cos beta=(c^2-(a^2+b^2))/(2*a*b)`

`cos beta=(100-(144+47.404))/(2*12*6.89)`

`cos beta=(100-191.404)/(165.36)`

`cos beta=(-91.404)/(165.36)`

`cos beta=-0.55275762`

`beta=123.56" deg"`