If a, b and c are three coplanar vectors. If a is not parallel to b, show that `c=(|[c*a, a*b], [c*b, b*b]|a+|[a*a, c*a], [a*b, c*b]|b)/(|[a*a, a*b], [a*b, b*b]|)`.

If a,b and c are any three vectors in space, then show that (c+b)xx(c+a)*(c+b+a)= [a b c]

If a, b, c are three given non-coplanar vectors and any arbitratry vector r is in space, where Delta_1=|[r*a, b*a, c*a], [r*b, b*b, c*b], [r*c, b*c, c*c]| : Delta_2=|[a*a, r*a, c*a], [a*b, r*b, c*b], [a*c, r*c, c*c]| Delta_3=|[a*a, b*a, r*a], [a*b, b*b, r*b], [a*c, b*c, r*c]|, Delta_4=|[a*a, b*a, c*a], [a*b, b*b, c*b], [a*c, c*c, c*c]| Q. The vector r is expressible in the form

Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

Show that |[a, b-c, c+b] , [a+c, b, c-a] , [a-b, b+a, c]|=(a+b+c)(a^2+b^2+c^2)

If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

If a, b and c are three non-coplanar vectors, then find the value of (a*(btimesc))/(ctimes(a*b))+(b*(ctimesa))/(c*(atimesb)) .

Show that: |[a,b-c,c+b],[a+c,b,c-a],[a-b,b+a,c]|=(a+b+c)(a^2+b^2+c^2) .

Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0

If a,b,c are three non-coplanar vectors, then 3a-7b-4c,3a-2b+c and a+b+lamdac will be coplanar, if lamda is