Distance of the point `P( vec p)` from the line ` vec r= vec a+lambda vec b` is a. `|( vec a- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)|` b. `|( vec b- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)|` c. `|( vec a- vec p)+((( vec p- vec b)dot vec b) vec b)/(| vec b|^2)|` d. none of these

Find | vec a| and | vec b| , if ( vec a+ vec b)dot(( vec a- vec b))=8 and |vec a|=8 | vec b|

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

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

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

The orthogonal projection of vec a\ on\ vec b is a. (( vec adot vec b) vec a)/(|"a"|^2) b. (( vec adot vec b) vec b)/(| vec b|^2) c. vec a/(| vec a|) d. vec b/(| vec b|)

Find | vec a|a n d| vec b|,if( vec a - vec b)dot ( vec a+ vec b) =27 and | vec a|=2| vec b|dot

For any two vectors vec a and vec b , show that : ( vec a+ vec b)dot( vec a- vec b)=0, when | vec a|=| vec b|dot

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

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 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