If the vectors (sec² A) are coplanar, then find the value of cosec²A A + cosec²B + cosec²C.

For three vectors to be coplanar we have

Which gives ^………(1)

^………(2)

Substituting equation 2 in 1 we have

Let

So we have

=(x-2)(y-2)(z-2)-(x-2)(y-1)(z-1)-(x-1)(y-2)(z-1)-(x-1)(y-1)(z-2)+2(x-1)(y-1)(z-1)=0

Solving we have x+y+z=4

Hence cosec²A + cosec²B + cosec²C = 4