Let ` vec r` be a unit vector satisfying ` vec rxx vec a= vec b ,w h e r e| vec a|=sqrt3a n d| vec b|=sqrt2.` Then

Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdot vec b= vec rdot vec c=0 for given non-zero vectors vec a , vec b and vec c dot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

Let vec a= hat i+ hat j ; vec b=2 hat i- hat kdot Then vector vec r satisfying vec rxx vec a= vec bxx vec a and vec rxx vec b= vec axx vec b then vecr is a. hat i- hat j+ hat k b. 3 hat i- hat j+ hat k c. 3 hat i+ hat j- hat k d. hat i- hat j- hat k

If vec a , vec ba n d vec c are unit vectors satisfying | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9, then |2 vec a+5 vec b+5 vec c| is.

If vec b is not perpendicular to vec c , then find the vector vec r satisfying the equyation vec rxx vec b= vec axx vec b and vec r. vec c=0.

Let vec r=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a),w h e r e vec a , vec ba n d vec c are there non-coplanar vectors. It is given that vec r is perpendicular to vec a+ vec b+ vec c , the minimum value of x^2+y^2 is equal to (A) pi^2 (B) (pi^2)/4 (C) (5pi^2)/4 (D) none of these

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""xxvec c""= vec b"" xxvec d"",vec a * vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

Let vec r , vec a , vec ba n d vec c be four nonzero vectors such that vec rdot vec a=0,| vec rxx vec b|=| vec r|| vec b|a n d| vec rxx vec c|=| vec r|| vec c|dot Then [abc] is equal to |a||b||c| b. -|a||b||c| c. 0 d. none of these

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q ,a n d vec r are parallel to vec a , vec b ,a n d vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to a. 1 b. 0 c. sqrt(3) d. 2

Given that vec a , vec b , vec p , vec q are four vectors such that vec a+ vec b=mu vec p , vec b*vec q=0a n d|vec b|^2=1,w h e r emu is a scalar. Then |( vec adot vec q) vec p-( vec pdot vec q) vec a| is equal to (a) 2| vec p . vec q| (b) (1//2)| vec p . vec q| (c) | vec pxx vec q| (d) | vec p . vec q|