Let ` hat a , hat b` ,and `hat c` be the non-coplanar unit vectors. The angle between ` hat b` and `hat c` is `alpha` , between ` hat c` and ` hat a` is `beta` and between ` hat a` and `hat b` is `gamma` . If `A( hat a cosalpha, 0),B( hat bcosbeta, 0)` and `C( hat c cosgamma, 0),` then show that in triangle `AB C ,` `(|hat axx(hat bxx hat c)|)/(sinA)=(|hat bxx(hat cxx hat a)|)/(sinB)=(|hat cxx(hat axx hat b)|)/(sinC)`