Prove that `[ vec l vec m vec n][ vec a vec b vec c]=| (vec l. vec a, vec l. vec b, vec l.vec c), (vec m. vec a, vec m. vec b, vec m.vec c),( vec n. vec a, vec n. vec b, vec n.vec c)|` .

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

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

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

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

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 (a) vec adot vec b+ vec bdot vec c+ vec c dot 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 c dot vec a (d). vec axx vec b+ vec bxx vec c+ vec cxx vec a=0

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)

Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. Let vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c]),a n d vec r=( vec axx vec b)/([ vec a vec b vec c]),dot If x in R^+, then a. x[ vec a vec b vec c]+([ vec p vec q vec r])/x has least value =2 . b. x^4[ vec a vec b vec c]^2+([ vec p vec q vec r])/(x^2) has least value =(3/2)^(2//3) c. [ vec p vec q vec r]>0 d. none of these

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

If vec x+ vec cxx vec y= vec aa n d vec y+ vec cxx vec x= vec b ,w h e r e vec c is a nonzero vector, then which of the following is not correct? a. vec x=( vec bxx vec c+ vec a+( vec c dot vec a) vec c)/(1+ vec c dot vec c) b. vec x=( vec cxx vec b+ vec b+( vec c dot vec a) vec c)/(1+ vec c dot vec c) c. vec y=( vec axx vec c+ vec b+( vec c dot vec b) vec c)/(1+ vec c dot vec c) d. none of these

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then