If ` vec aa n d vec b` are two vectors, then prove that `( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b|` .

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

Prove that if [ vec l vec m vec n] are three non-coplanar vectors, then [ vec l vec m vec n]( vec axx vec b)=| vec ldot vec a vec ldot vec b vec l vec mdot vec a vec mdot vec b vec m vec ndot vec a vec ndot vec b vec n| .

If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k , then find the vaue of | vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec a vec bdot vec a vec cdot vec a vec cdot vec a vec cdot vec a| .

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec cdot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec cdot vec d=0

If vec a , vec b , vec c are three given non-coplanar vectors and any arbitrary vector vec r in space, where Delta1=| vec rdot vec a vec bdot vec a vec cdot vec a vec rdot vec b vec bdot vec b vec cdot vec b vec rdot vec c vec bdot vec c vec cdot vec c| , Delta2=| vec adot vec a vec rdot vec a vec cdot vec a vec adot vec b vec rdot vec b vec cdot vec b vec adot vec c vec rdot vec c vec cdot vec c| Delta3=| vec adot vec a vec bdot vec a vec rdot vec a vec adot vec b vec bdot vec b vec rdot vec b vec adot vec c vec bdot vec c vec rdot vec c| , Delta =| vec adot vec a vec bdot vec a vec cdot vec a vec adot vec b vec bdot vec b vec cdot vec b vec adot vec c vec bdot vec c vec cdot vec c| , then prove that vec r=(Delta1)/ Deltavec a+(Delta2)/Delta vec b+(Delta3)/Delta vec c .

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 vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=3\ a n d\ vec adot vec b=1, find the angle between.

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