Find the magnitude of two vectors `veca` and `vec b` having the same magnitude such that the angle between them is `30^(@)` and their scalar product is` sqrt3`.

Answer

100 unit at `45^@` with x axis

Explanation

x coponents of `vecA=100 cos 45^@ =100/sqrt(2)unit`
x component of `vecB cos 135^@= - 100/sqrt(2)`
x component of `vecC=100 cos 315^@, =100 cos 45^@ = 100/sqrt(2)`
Resultant x component, `=100/(sqrt/)-100/sqrt(2)+100/sqrt(2)=100/sqrt(2)`

Now, y component of `vecA=100 sin 45^@=100/sqrt(2)`
y component of `vecB=100 sin 135^@=100/sqrt(2)`
y component of `vecC=100 sin 135^@=100/sqrt(2),` Resultant y component, `=100/sqrt(2)+100/sqrt(2)-100/sqrt(2)`
`=100/sqrt(2), Resultant= sqrt((100/sqrt(2))^+(100/sqrt(2))^2)`
`sqt(1000)=100`, `tan alpha =(ycomp)/(xcomp)
(100sqrt(2))/(100(sqrt(2))=1`
` rarr alpha=tan^-1(1)=45^@ The resultant is 100 unit at 45^@ with x axis.`