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]`

( 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]

If vec a , vec b ,a n d vec c are three non-coplanar vectors, then find the value of ( vec a .( vec bxx vec c))/( vec b .( vec cxx vec a))+( vec b .( vec cxx vec a))/( vec c .( vec axx vec b))+( vec c . ( vec bxx vec a))/( vec a . ( vec bxx vec c))

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec b . vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec c . vec a)/(| vec a|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec c . vec a)/(| vec a|^2) vec a-( vec b . vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec c . vec a)/(| vec c|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec c . vec a)/(| vec c|^2) vec a=( vec b . vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is a. ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

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

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

vec a , vecb , vec c are three mutually perpendicular unit vectors then |vec a + vec b + vec c| is equal to

If vec a , vec ba n d vec c are non-coplanar vectors, prove that the four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+ 4 vec b-2 vec ca n d vec a-6 vec b+6 vec c are coplanar.

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.

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

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| .