The vectors `vec a` and `vec b` are non collinear. If `vec p = (x+4y)veca+ (2x+y+1)vec b` and `vec q= (-2x+y+2)vec a+ (2x-3y-1)vec b` satisfy the relation `3vec p= 2vec q` find the values of x and y.

The vectors vec(a) " and " vec(b) are non-collinear. If vec(p)=(x+4y)vec(a)+(2x+y+1)vec(b) and vec(q)=(-2x+y+2)vec(a)+(2x-3y-1)vec(b) satisfy the relation 3vec(p)=2vec(q) , find the values of x and y.

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?

The vectors vec(a) " and " vec(b) are non-collinear. Find for what value of x, the vectors vec(c)=(x-7)vec(a)+2vec(b) "and " vec(d)=(2x+1)vec(a)-vec(b) are collinear.

vec a, vec ba n d vec c are non-collinear if vec axx( vec bxx vec c)+( vec a. vec b) vec b=(4-2x-sin y) vec b+(x^2-1) vec c and ( vec c . vec c) vec a= vec c 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 a , vec b , and vec c be non-zero vectors such that no two 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 b and vecc , then find the value of sin thetadot

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] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

If | vec a|=2| vec b|=5 and | vec axx vec b|=8, then find the value of vec a . vec bdot

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 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)| = 2, |vec(b)| = 3 and vec (a) . vec(b) = 3 , then find the projection of vec(b)" on " vec(a)