`A B C D` parallelogram, and `A_1a n dB_1` are the midpoints of sides `B Ca n dC D ,` respectivley . If ` vec A A_1+ vec A B_1=lambda vec A C ,t h e nlambda` is equal to a. `1/2` b. `1` c. `3/2` d. `2` e. `2/3`

ABCD is a parallelogram and A_(1) " and " B_(1) are the midpoints of sides BC and CD respectively. If vec(A""A_(1))+vec(AB_(1))=lambda/2vec(AC) , then lambda is equal to -

If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n dB D respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

G is the centroid of triangle ABC and A_1 and B_1 are the midpoints of sides AB and AC , respectively. If Delta_1 is the area of quadrilateral G A_1A B_1 and Delta is the area of triangle ABC , then Delta/Delta_1 is equal to a. 3/2 b. 3 c. 1/3 d. none of these

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

If vec aa n d vec b are two unit vectors incline at angle pi//3 , then { vec axx( vec b+ vec axx vec b)}dot vec b is equal to (-3)/4 b. 1/4 c. 3/4 d. 1/2

If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec G C is equal to a. vec0 b. 3 vec G A c. 3 vec G B d. 3 vec G C

ABCDE is a pentagon. Prove that the resultant of force vec A B , vec A E , vec B C , vec D C , vec E D and vec A C ,is 3 vec A C .

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

Let vec a , vec b a n d vec c be three vectors having magnitudes 1, 5and 3, respectively, such that the angel between vec aa n d vec bi stheta and vec axx( vec axx vec b)=c . Then t a ntheta is equal to a. 0 b. 2/3 c. 3/5 d. 3/4

vec a , vec b , and vec c are three vectors of equal magnitude. The angle between each pair of vectors is pi//3 such that | vec a+ vec b+ vec c|=sqrt6. Then | vec a| is equal to a. 2 b. -1 c. 1 d. sqrt(6)//3