`A ,B ,C and D` have position vectors ` vec a , vec b , vec c` and `vec d ,` respectively, such that ` vec a- vec b=2( vec d- vec c)dot` Then a. `A Ba n dC D` bisect each other b. `B Da n dA C` bisect each other c. `A Ba n dC D` trisect each other d. `B Da n dA C` trisect each other

For any four vectors, vec a , vec b , vec c and vec d prove that vec d.( vec axx( vec bxx( vec cxx vec d)))=( vec b. vec d)[ vec a \ vec c \ vec d] .

If vec a , vec b ,a n d vec c are non-zero vectors such that vec a. vec b= vec a. vec c , then find the geometrical relation between the vectors.

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

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

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c. vec b

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of | vec a+ vec b+ vec c |