Three distinct points `P(3u^(2),2u^(3));Q(3v^(2),2v^(3))` and `R(3w^(2),2w^(3))` are collinear then `uv+vw+wu` is equal to

Show that the points P (-2, 3, 5) , Q (1, 2, 3) and R (7, 0, -1) are collinear.

(3p^(2)qr^(3)) xx (- 4p^(3)q^(2)r^(2))xx (7pq^(2)r) is equal to

(3+omega + 3 omega^(2))^(4)= lambda omega , then value of lambda is :

If A= ((1,0,0),(2,1,0),(3,2,1)), U_(1), U_(2), and U_(3) are column matrices satisfying AU_(1) =((1),(0),(0)), AU_(2) = ((2),(3),(0))and AU_(3) = ((2),(3),(1)) and U is 3xx3 matrix when columns are U_(1), U_(2), U_(3) then answer the following questions The value of (3 2 0) U((3),(2),(0)) is

Let hat(u), hat(v) and hat(w) are three unit vectors, the angle between hat(u) and hat(v) is twice that of the angle between hat(u) and hat(w) and hat(v) and hat(w) , then [hat(u) hat(v) hat(w)] is equal to

Statement 1 : The chord of contact of the circle x^2+y^2=1 w.r.t. the points (2, 3), (3, 5), and (1, 1) are concurrent. Statement 2 : Points (1, 1), (2, 3), and (3, 5) are collinear.

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

Fig shows three resistor configuration R_(1), R_(2) and R_(3) connected to 3V battery. If the power dissipated by the configuration R_(1), R_(2) and R_(3) is P_(1), P_(2) and P_(3) respectively, then

(20u^(3)v6(2)-15u^(2)v)/(10u^(4)v+30u^(3)v^(3)) Which of the following is the reduced form of the expression above?

If 3u+w=7 and 3k-9u=2, what is the value of w+k?