If ` vec a , vec b and vec c` are three non-zero vectors, no two of which are collinear, ` vec a+2 vec b` is collinear with `vec c` and ` vec b+3 vec c` is collinear with ` vec a ,` then find the value of `| vec a+2 vec b+6 vec c|`.

Given three vectors vec a , vec b ,a n d vec c two of which are non-collinear. Further if ( vec a+ vec b) is collinear with vec c ,( vec b+ vec c) is collinear with vec a ,| vec a|=| vec b|=| vec c|=sqrt(2)dot Find the value of vec a. vec b+ vec b. vec c+ vec c. vec a a. 3 b. -3 c. 0 d. cannot be evaluated

If vec a , vec b and vec c are any three non-coplanar vectors, then prove that points are collinear: veca+ vecb+vecc , 4veca+3vecb ,10veca+7vec b-2vecc .

Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of them are collinear. If the vector (vec(a)+vec(b)) is collinear with the vector vec(c) and the vector (vec(b)+vec(c)) is collinear with vector vec(a) , then prove that (vec(a)+vec(b)+vec(c)) is a null vector.

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

If vec a and vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a and vec b .

If vec a , vec b , and vec c be non-zero vectors such that no two are collinear or ( vec axx vec b)xx vec c=1/3| vec b|| vec c| vec adot If theta is the acute angle between vectors vec b and vecc , then find the value of sin thetadot

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

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

If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

If vec(a) and vec(b) are two vector such that |vec(a)| = 2, |vec(b)| =3 and vec(a).vec(b) =4 , then find the value of |vec(a)- vec(b)|