Question

let e1 and e2 be unit vectors containing angle x.
then,
1/2[e1-e2]=sinkx

Answer 1

Since e1 and e2 are unit vectors and angle between them is x


Therefore,
|e1 - e2| = sqrt(e1² + e2² -2cosx) {e1 and e2 are unit vectors e1²=e2²=1}
|e1 - e2| = sqrt(2-2cosx) Since, cosx = 1 - 2 sin²(x/2)
|e1 - e2| = sqrt(2 - 2 + 4sin²(x/2)
|e1 - e2| = sqrt(4sin²(x/2))
|e1 - e2| = 2sin(x/2)

½|e1 - e2| = sin(x/2) = sin kx

=> k=½