Let `hata,vecb and vecc` be the non-coplanar unit vectors. The angle between `hatb and hatc is alpha "between" hatc and hata is beta and "between" hata and hatb is gamma`. If `A(hatacos alpha),B(hatbcosbeta) and C(hatc cosgamma),` then show that in triangle ABC, `(|hataxx(hatbxxhatca)|)/(sinA)=(|hatbxx(hatcxxhata)|)/sinB = (|hatcxx(hataxxhatb)|)/sinC=(prod|hataxx(hat xx hatc|))/(sumsin alpha-cosbeta. cos gammahatn_(1))` where `hatn_(1)=(hatbxxhatc)/(|hatbxxhatc|),hatn_(2)=(hatcxxhata)/(|hatcxxhata|)and hatn_(3)=(hataxxhatb)/(|hataxxhatb|)`