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

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

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 adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

Find |vec a| and |vec b|,quad if (vec a-vec b)vec a+vec b=27 and |vec a|=2|vec b|

if | vec a | = | vec b | then find [(vec a + vec b) * (vec a-vec b)]

find | vec a |, | vec b | if (vec a + vec b) * (vec a-vec b) = 8 and | vec a | = 8 | vec b |

If vec p = vec a + vec b, vec q = vec a-vec b | vec a | = | vec b | = 1 then | vec p xxvec q | =

If non-zero vectors vec aa n d vec b are equally inclined to coplanar vector vec c ,t h e n vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these