If vectors ` vec a and vec b` are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to `veca` is a.` vec b+( vec bxx vec a)/(| vec a|^2)` b. `( vec a. vec b)/(| vec b|^2)` c. ` vec b-(( vec b. vec a)veca)/(| vec a|^2)` d. `( vec axx( vec bxx vec a))/(| vec b|^2)`

If vectors vec aa n d vec b are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to a is a. vec b+( vec bxx vec a)/(| vec a|^2) b. ( vec adot vec b)/(| vec b|^2) c. vec b-( vec bdot vec a)/(| vec a|^2) d. ( vec axx( vec bxx vec a))/(| vec b|^2)

The vector component of vec b perpendicular to vec a is a. ( vec bdot vec c) vec a b. ( vec axx( vec bxx vec a))/(| vec a|^2) c. vec axx( vec bxx vec a) d. none of these

If vec adot vec b=betaa n d vec axx vec b= vec c ,t h e n vec b is ((beta vec a- vec axx vec c))/(| vec a|^2) b. ((beta vec a+ vec axx vec c))/(| vec a|^2) c. ((beta vec c- vec axx vec c))/(| vec a|^2) d. ((beta vec a+ vec axx vec c))/(| vec a|^2)

If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec c , we may have a. ( vec a. vec c)| vec b|^2=( vec a. vec b)( vec b.vec c)( vec c.vec a) b. vec adot vec b=0 c. vec adot vec c=0 d. vec bdot vec c=0

( vec a+2 vec b- vec c)dot{( vec a- vec b)xx( vec a- vec b- vec c)} is equal to [ vec a\ vec b\ vec c] b. c. 2[ vec a\ vec b\ vec c] d. 3[ vec a\ vec b\ vec c]

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= a. 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

For any three vectors veca , vec b , vec c show that vecaxx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)= vec0

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

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] .

For any three vectors vec a , vec b , vec c , prove that | vec a+ vec b+ vec c|^2=| vec a|^2+| vec b|^2+| vec c|^2+2( vec adot vec b+ vec bdot vec c+ vec cdot vec a)