Let `vecA and vecB` be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles `30^@ and 60^@` respectively, find the resultant.

Answer

19.3

Explanation

Angle between `vecA and vecB=is theta`
`= 60^@-30^@`=`30^@`
`|vecA|=|vecB|=10 unit` R=`sqrt(10^2+10^2+2.10.10 cos 30^-0)`
=`sqrt(200+200cos 30^0)`
`=sqrt(200+100)`
=`sqrt(300)=19.3`

Let `beta= the angle between vecR and vecA`, `beta=tan^-1((10 sin 30^0)/(10+10 cos 30^0))`
=`tan^-1(1/(2+sqrt(3)))= tan^-1(1/(3.372))`
=`tan^-1(0.26795)=15^0`
Resultant makes angle, `=15^0+30^0`
`=45^0` with x-axis.