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 c dot vec d` c. ` vec bdot vec c+ vec adot vec d=0` d. ` vec adot vec b+ vec c dot vec d=0`

Line vec r= vec a+lambda vec b will not meet the plane vec rdot vec n=q , if a. vec bdot vec n=0, vec adot vec n=q b. vec bdot vec n!=0, vec adot vec n!=q c. vec bdot vec n=0, vec adot vec n!=q d. vec bdot vec n!=0, vec adot vec n=q

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

If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b+ vec c= vec0 find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot'

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c and vec a is not a zero vector. Show that vec b= vec c dot

Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec adot vec d)[ vec a vec b vec c] b. ( vec adot vec c)[ vec a vec b vec d] c. ( vec adot vec b)[ vec a vec b vec d] d. none of these

If vec a , vec b ,a n d vec c are unit vectors such that vec a+ vec b+ vec c=0, then find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot

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

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 dot vec c dot vec a dot vec c dot vec a dot vec c dot vec a| .

The lines vec r= vec a+lambda( vec bxx vec c)a n d vec r= vec b+mu( vec cxx vec a) will intersect if a. vec axx vec c= vec bxx vec c b. vec adot vec c= vec bdot vec c c. bxx vec a= vec cxx vec a d. none of these

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)