`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`

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

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

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

A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD C respectively, then express vec A La n d vec A M in terms of vec A Ba n d vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot

A straight line L cuts the lines A B ,A Ca n dA D of a parallelogram A B C D at points B_1, C_1a n dD_1, respectively. If ( vec A B)_1,lambda_1 vec A B ,( vec A D)_1=lambda_2 vec A Da n d( vec A C)_1=lambda_3 vec A C , then prove that 1/(lambda_3)=1/(lambda_1)+1/(lambda_2) .

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

A B C D isa parallelogram with A C\ a n d\ B D as diagonals. Then, vec A C- vec B D= 4 vec A B b. 3 vec A B c. 2 vec A B d. vec A B

If | vec axx vec b|=4,\ vec adot vec b =2,\ t h e n\ | vec a|^2| vec b|^2= 6 b. 2 c. 20 d. 8

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

In triangle A B C , if sinAcosB=1/4a n d3t a n A=t a n B ,t h e ncot^2A is equal to 2 (b) 3 (c) 4 (d) 5.