Let the sides of a parallelogram be U=a, U=b,V=a' and V=b', where U=lx+my+n, V=l'x+m'y+n'. Show that the equation of the diagonal through the point of intersection of
`U=a, V=a' and U=b, V=b' " is given by " |{:(U,V,1),(a,a',1),(b,b',1):}| =0.`

Let the sides of a parallelogram be U=a, U=b,V=a' and V=b' , where U=lx+my+n, V=l'x+m'y+n' . Show that the equation of the diagonal through the point of intersection of U=a,V=a' and U=b,V=b' is given by det [[U,a,b],[V,a',b'],[1,1,1]] =0 .

Verify the correctness of the equations v = u + at .

The table given below shows the position of element U, V, X, Y and Z. Which is larger in size V or X

If the string is inextensible, determine the velocity u of each block in terms of v and theta . (a) fig a: u=… (b) fig.(b): u=….

If y=(u)/(v) , where u and v are functions of x, show that v^(3)(d^(2)y)/(dx^(2))=|{:(u,v,0),(u',v,v),(u'',v'',2v'):}| .

If a ,b,c, and u,v,w are complex numbers representing the vertices of two triangle such that they are similar, then prove that (a-c)/(a-b) =(u-w)/(u-v)

Two particles are projected from a point at the same instant with velocities whose horizontal and vertical components are u_(1), v_(1) and u_(2), v_(2) respectively. Prove that the interval between their passing through the other common point of their path is (2(v_(1)u_(2) - v_(2) u_(1)))/(g (u_(1) + u_(2))

Solve the following system of equations: 8v-3u=5u v ,\ \ \ 6v-5u=-2u v

Let u-=a x+b y+a b3=0,v-=b x-a y+b a3=0,a ,b in R , be two straight lines. The equations of the bisectors of the angle formed by k_1u-k_2v=0 and k_1u+k_2v=0 , for nonzero and real k_1 and k_2 are