Given three non-zero, non-coplanar vectors ` vec a , vec b ,and vecc .vec r_1=p vec a+q vec b+ vec ca n d vec r_2= vec a+p vec b+q vecc dot` If the vectors ` vec r_1+2 vec r_2 and 2 vec r_1+ vec r_2` are collinear, then `(p ,q)` is `

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec b . vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec c . vec a)/(| vec a|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec c . vec a)/(| vec a|^2) vec a-( vec b . vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec c . vec a)/(| vec c|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec c . vec a)/(| vec c|^2) vec a=( vec b . vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is a. ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c and vec a is not a zero vector. Show that vec b= vec c dot

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

For non-zero vectors vec(a) and vec(b), " if " |vec(a) + vec(b)| lt |vec(a) - vec(b)| , then vec(a) and vec(b) are-

Let vec a , vec b ,a n d vec c be non-zero vectors and vec V_1= vec axx( vec bxx vec c)a n d vec V_2=( vec axx vec b)xx vec c. Vectors vec V_1a n d vec V_2 are equal. Then (a). vec aa n vec b are orthogonal (b). vec aa n d vec c are collinear (c). vec ba n d vec c are orthogonal (d). vec b=lambda( vec axx vec c)w h e nlambda is a scalar

If vec a , vec ba n d vec c are non-coplanar vectors, prove that the four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+ 4 vec b-2 vec ca n d vec a-6 vec b+6 vec c are coplanar.

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 r . vec a= vec r . vec b= vec r . vec c=0,w h e r e vec a , vec b ,and vec c are non-coplanar, then a. vec r_|_( vec cxx vec a) b. vec r_|_( vec axx vec b) c. vec r_|_( vec bxx vec c) d. vec r= vec0