Find each of the products: `(4/3u^2v w)xx\ (-5u v w^2)xx(1/3v^2w u)`

Solve the following system of equations: 2(3u-v)=5u v ,\ \ \ \ 2(u+3v)=5u v

Solve the following system of equations: (15)/u+2/v=17 ,\ \ \ 1/u+1/v=(36)/5

If vec u , vec v and vec w are three non-coplanar vectors, then prove that ( vec u+ vec v- vec w) . [ [( vec u- vec v)xx( vec v- vec w)]]= vec u . vec v xx vec w

If vec u , vec v and vec w are three non-cop0lanar vectors, then prove that ( vec u+ vec v- vec w)dot [( vec u- vec v)xx( vec v- vec w)] = vec u dot (vec v xx vec w)

Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations u+2v+3w=6,4u+5v+6w=12 and 6u+9v=4 . Further consider the expressions f(x)=(1/u+1/v+1/w)x^(2)+[(b-c)^(2)+(c-a)^(2)+(x-b)^(2)] x+u+v+w=0 and g(x)=20x^(2)+10(a-d)^(2)x-9=0 (u+v+w) is equal to

Let y = uv be the product of the functions u and v . Find y'(2) if u(2) = 3, u'(2) = – 4, v(2) = 1, and v'(2) = 2.

If u and v are complex numbers such that u=3-5i and v=-6+i , which of the following is equivalent to (u+v)^(2) ? (Note: i^(2)=-1 )

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2y +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.