Question

11. A vector A is expressed as A = Avi + AJJ where Ayand Ay are its components
along r- axis and y - axis respectively. If vector A makes an angle ( with x -
axis, then O is given by which expression?​

Answer 1

Let the vector is A having magnitude a and making an angle x with x axis.so, the components are

  acosx=n+1

 asinx=1

When coordinates are rotated by 600, the angle can be x+60orx−60 ,the new coordinates are

  acos(x±60)=n

 asin(x±60)=3

Now, solving four equations we get

  acos(x±60)=a(cosxcos60±sinxsin60)

 n=a(21cosx±23sinx)

 put,acosx=n+1andasinx=1

 so,n=1±3

n depends on direction of rotation.