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]|)`.

bar(a),bar(b),bar(c ) are three coplanar vectors, If bar(a) is not parallel to bar(b) , Show that

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 and c are unit coplanar vectors, then [[2a-b, 2b-c, 2c-a]] is equal to

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 as

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