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 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.

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

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= a. [ vec a\ vec b\ vec c] b. 0 c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

If vec r . vec a= vec r . vec b= vec r . vec c=0,w h e r e vec a , vec b ,and vec c are non-coplanar, then a. vec r_|_( vec cxx vec a) b. vec r_|_( vec axx vec b) c. vec r_|_( vec bxx vec c) d. vec r= vec0

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c . Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

If vec a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .

Let vec a , vec b and vec c be three non-zero vectors such that vec a+ vec b+ vec c=0 and lambda vec bxx vec a+ vec bxx vec c+ vec cxx vec a=0, then find the value of lambda