If `D ,Ea n dF` are three points on the sides `B C ,C Aa n dA B ,` respectively, of a triangle `A B C` such that AD,BE and CF are concurrent, then show that `(B D)/(C D),(C E)/(A E),(A F)/(B F)=-1`

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

From the given figures identify the A,B,C,D,E and F

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than quadrilateral A B C D is a ;

In an acute triangle A B C if sides a , b are constants and the base angles Aa n dB vary, then show that (d A)/(sqrt(a^2-b^2sin^2A))=(d B)/(sqrt(b^2-a^2sin^2B))

If in a triangle A B C , the side c and the angle C remain constant, while the remaining elements are changed slightly, using differentials show that (d a)/(cosA)+(d b)/(cosB)=0

Statement 1: if three points P ,Qa n dR have position vectors vec a , vec b ,a n d vec c , respectively, and 2 vec a+3 vec b-5 vec c=0, then the points P ,Q ,a n dR must be collinear. Statement 2: If for three points A ,B ,a n dC , vec A B=lambda vec A C , then points A ,B ,a n dC must be collinear.

If a,b,c,d,e,f are in A.P. then d-b= ……

In a right triangle with legs a and b and hypotenuse c, angles A,B and C are opposite to the sides a,b and c respectively, then e^(lnb-lna) is equal to-