If ` vec a , vec b` are two non-collinear vectors, prove that the points with position vectors ` vec a+ vec b , vec a- vec b` and ` vec a+lambda vec b` are collinear for all real values of `lambdadot`

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.

For any vectors vec a vec b , show that |vec a + vec b| le |vec a| + |vec b| .

If vec a and vec b are collinear vectors, then which of the following are incorrect?

If vec a and vec b are two non- zero vectors such that | vec a + vec b| = |vec a - vec b| , then show that vec a and vec b are perpendicular.

For any two vectors veca and vec b show that |vec a. vec b| le |vec a||vec b| .

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 aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

If vec a , vec b , vec c are non-coplanar vector and lambda is a real number, then the vectors vec a+2 vec b+3 vec c ,lambda vec b+mu vec ca n d(2lambda-1) vec c are coplanar when a. mu in R b. lambda=1/2 c. lambda=0 d. no value of lambda

Vectors vec a and vec b are non-collinear. Find for what value of n vectors vec c=(n-2) vec a+ vec b and vec d=(2n+1) vec a- vec b are collinear?

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)