Prove that a necessary and sufficient condition for three vectors ` vec a , vec b` and ` vec c` to be coplanar is that there exist scalars `l , m , n` not all zero simultaneously such that `l vec a+m vec b+n vec c= vec0dot`

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is 0 b. 1 c. -sqrt(3) d. sqrt(3)

If vec a , vec b , and vec c are mutually perpendicular vectors of equal magnitudes, then find the angle between vectors vec a and vec a+ vec b+ vec c dot

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of | vec a+ vec b+ vec c |

The scalars l and m such that l vec a+m vec b= vec c ,where vec a , vec b and vec c are given vectors, are equal to

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then 1. vec a , vec b ,a n d vec c can be coplanar 2. vec a , vec b ,a n d vec c must be coplanar 3. vec a , vec b ,a n d vec c cannot be coplanar 4.none of these

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

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

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

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)