If `a + b +c =9 and ab + bc + ca =26,` then find `a ^(2) + b ^(2) + c ^(2).`

If a+b+c=9 and ab + bc + ca = 26, find a^2 + b^2 +c^2.

If a + b + c = 12 and ab + bc + ca = 47 , find a^2 + b^2 + c^2 .

If a,b,c are in H.P and ab + bc ca = 15, then ca =

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

If a,b,c are three vectors such that a + b + c = 0, |a| = 1, |b| = 2, |c| = 3 then a.b+ b.c + c.a =