`A B C D` parallelogram, and `A_1a n dB_1` are the midpoints of sides `B Ca n dC D ,` respectivley . If ` vec AA_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`

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

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

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

If a :(b+c)=1:3 a n d c :(a+b)=5:7, t h e b :(a+c) is equal to 1:2 b. 1:3 c. 2:3 d. 2:1

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) .

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) .

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) .

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) .

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 1/(lambda_3) .

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