If ` vec a , vec ba n d vec c` are three non-zero vectors, no two of which ar 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|dot`

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 axx vec b)^2+( vec a dot vec b)^2=144a n d| vec a|=4, then find the value of | vec b|dot

If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3vec a-7 vec b-4 vec c ,3 vec a -2 vec b+ vec c and vec a + vec b +2 vec c are coplanar.

If vec a , vec b ,a n d vec c be non-zero vectors such that no tow 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 ba n d vecc , then find the value of sin thetadot

If vec a ,a n d 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 ,a n d vec bdot

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

If vec a , vec b ,a n d vec c are there mutually perpendicular unit vectors and vec d is a unit vector which makes equal angles with vec a , vec b ,a n d vec c , the find the value off | vec a+ vec b+ vec c+ vec d|^2dot

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot