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?

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.

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

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

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

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.

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

vec b a n d vec c are non-collinear if vec axx( vec bxx vec c)+( vec adot vec b) vec b=(4-2x-sin y) vec b+(x^2-1) vec c and ( vec c . vec c) vec a= vec c dot Then a. x=1 b. x=-1 c. y=(4n+1)pi//2, n in I d. y=(2n+1)pi//2, n in I

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| .

vec aa n d vec b are two non-collinear unit vector, and vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec bdot Then | vec v| is | vec u| b. | vec u|+| vec udot vec b| c. | vec u|+| vec udot vec a| d. none of these