In a trapezium, vector ` vec B C=alpha vec A Ddot` We will then find that ` vec p= vec A C+ vec B D` is collinear with` vec A Ddot` If ` vec p=mu vec A D ,` then which of the following is true? a. `mu=alpha+2` b. `mu+alpha=2` c. `alpha=mu+1` d. `mu=alpha+1`

In a trapezium ABCD the vector B vec C = lambda vec(AD). If vec p = A vec C + vec(BD) is coillinear with vec(AD) such that vec p = mu vec (AD), then

vec a, vec b, vec c, dare any four vectors then (vec a xxvec b) xx (vec c xxvec d) is a vector Perpendicular to vec a, vec b, vec c, vec d

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

If vec a, vec b, vec c and vec d are unit vectors such that (vec a xxvec b) * (vec c xxvec d) = 1 and vec a * vec c = (1) / (2)

If vec a , vec b , vec c and vec d are the position vectors of points A, B, C, D such that no three of them are collinear and vec a + vec c = vec b + vec d , then ABCD is a

If quad vec r = alpha (vec b xxvec c) + beta (vec c xxvec a) + gamma (vec a xxvec b) and [vec with bvec c] = 2 then alpha + beta + gamma

If vec a , vec b , vec c , vec d are non-zero, non collinear vectors and if ( vec ax vec b)x( vec cx vec d)dot( vec ax vec d)=0 , then which of the following is always true. vec a , vec b , vec c , vec d are necessarily coplanar either vec a or vec d must lie in the plane of vec b and vec c either vec b or vec c must lie in plane of vec a and vec d either vec a or vec b must lie in plane of vec c and vec d

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

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]