`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) .

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

For any two vectors vec a\ a n d\ vec b , fin d\ ( vec axx vec b). vecbdot

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 two vectors vec aa n d vec b are such that |veca|=3, |vecb|=2 and veca.vecb=6, . , Find | vec a+ vec b|a n d| vec a- vec b|dot

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]

For any three vectors adotb\ a n d\ c write the value of vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot

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 prove that quadrilateral A B C D is a parallelogram.

If vec a a n d vec b are two vectors such that vec adot vec b=6, | vec a|=3 a n d | vec b|=4. Write the projection of vec a on vec bdot

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