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 ` vec r` =?

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.

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

If vec a, vec b, vec c are unit vectors satisfying the condition veca+ vec b+ vec c= 0 then show that vec a. vec b+ vec b.vec c+ vec c. vec a= -3//2 .

If vec a , vec b ,a n d vec c are such that [ vec a vec b vec c]=1, vec c=lambda vec axx vec b , , | vec a|=sqrt(2),| vec b|=sqrt(3)a n d| vec c|=1/(sqrt(3)) , then the angle between vec a and vec b is pi/6 b. pi/4 c. pi/3 d. pi/2

A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b ,w h e r e| vec a|=6a n d| vec b|=8,a n d vec aa n d vec b are anti-parallel. Then the length of the longer diagonal is 40 b. 64 c. 32 d. 48

A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b ,w h e r e| vec a|=6a n d| vec b|=8,a n d vec aa n d vec b are anti-parallel. Then the length of the longer diagonal is 40 b. 64 c. 32 d. 48

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

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x