If ` vec u ,"" vec v , vec w` are noncoplanar vectors and p, q are real numbers, then the equality `[3 vec u ,""p vec v , p vec w]-[p vec v ,"" vec w , q vec u]-[2 vec w ,""q vec v , q vec u]=0` holds for (1) exactly one value of (p, q) (2) exactly two values of (p, q) (3) more than two but not all values of (p, q) (4) all values of (p, q)

If vec u , vec v , vec w are noncoplanar vectors and p, q are real numbers, then the equality [3 vec u ,""p vec v , p vec w]-[p vec v ,"" vec w , q vec u]-[2 vec w ,""q vec v , q vec u]=0 holds for (A) exactly one value of (p, q) (B) exactly two values of (p, q) (C) more than two but not all values of (p, q) (D) all values of (p, q)

If vec u , vec v and vec w are three non-cop0lanar vectors, then prove that ( vec u+ vec v- vec w)dot [( vec u- vec v)xx( vec v- vec w)] = vec u dot (vec v xx vec w)

If vec u , vec v and vec w are three non-coplanar vectors, then prove that ( vec u+ vec v- vec w) . [ [( vec u- vec v)xx( vec v- vec w)]]= vec u . vec v xx vec w

Let vec u and vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec v . Find the value of [ vec u \ vec v \ vec w] .

Let vec a, vec b, and vec c be three non coplanar unit vectors such that the angle between every pair of them is pi/3 . If vec a xx vec b+ vecb xx vec x=p vec a + q vec b + r vec c where p,q,r are scalars then the value of (p^2+2q^2+r^2)/(q^2) is

Let vec a, vec b, and vec c be three non coplanar unit vectors such that the angle between every pair of them is pi/3 . If vec a xx vec b+ vecb xx vec c=p vec a + q vec b + r vec c where p,q,r are scalars then the value of (p^2+2q^2+r^2)/(q^2) is

Let vec ua n d vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec vdot Find the value of [ vec u vec v vec w]dot

Let vec u , vec v and vec w be vector such vec u+ vec v+ vec w= vec0 . If | vec u|=3,| vec v|=4 and | vec w|=5, then find vec u . vec v+ vec v . vec w+ vec w . vec u .

If vec a and vec b are non-collinear vectors and vec A=(p+4q) vec a+(2p+q+1) vec b a n d vec B=(-2p+q+2) vec a+(2p-3q-1) vec b ,a n d if 3 vec A=2 vec B , then determine p and q.

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3