Let `a , ba n dc` detnote the sides `B C ,C Aa n dA B` respectively of ` A B Cdot` If `|1a b1c a1b c|=0`

Let a , band c detnote the sides BC,CA andAB respectively of triangle ABC. If |[1,a, b],[1,c, a],[1,b ,c]|=0. find the value of sin^2A+sin^2B+sin^2C

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 vec adot vec b+ vec bdot vec c+ vec cdot vec a=0 b. vec axx vec b= vec bxx vec c= vec cxx vec a c. vec adot vec b= vec bdot vec c= vec cdot vec a d. vec axx vec b+ vec bxx vec c+ vec cxx vec a=0

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

In triangle A B C ,poin t sD , Ea n dF are taken on the sides B C ,C Aa n dA B , respectigvely, such that (B D)/(D C)=(C E)/(E A)=(A F)/(F B)=ndot Prove that _(D E F)=(n^2-n+1)/((n+1)^2)_(A B C)dot

If a ,b ,c denote the lengths of the sides of a triangle opposite to angles A ,B ,C respectively of a A B C , then the correct relation among a ,b , cA ,Ba n dC is given by (b+c)sin((B+C)/2)=acos b. (b-c)cos(A/2)=asin((B-C)/2) c. (b-c)cos(A/2)=2asin((B-C)/2) d. (b-c)sin((B-C)/2)="a c o s"A/2

In a A B C , If L a n d M are points on A B a n d A C respectively such that L M B Cdot Prove that: a r ( A B M)=a r ( A C L)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L C M)=a r\ ( L B M)

G is the centroid of triangle A B Ca n dA_1a n dB_1 are rthe midpoints of sides A Ba n dA C , respectively. If "Delta"_1 is the area of quadrilateral G A_1A B_1a n d"Delta" is the area of triangle A B C , then "Delta"//"Delta"_1 is equal to a.3/2 b. 3 c. 1/3 d. none of these