If ` vec a ,\ vec b ,\ vec c` are non coplanar vectors, prove that the following vectors are non coplanar:`\ vec a+2 vec b+3 vec c ,\ 2 vec a+ vec b+3 vec c\ a n d\ vec a+ vec b+ vec c`

If vec a ,\ vec b ,\ vec c are non coplanar vectors, prove that the following vectors are non coplanar: \ 2 vec a- vec b+3 vec c ,\ vec a+ vec b-2 vec c\ a n d\ vec a+ vec b-3 vec c

If a ,\ b ,\ c are non zero non coplanar vectors, prove that the following vectors are coplanar. 5 vec a+6 vec b+7 vec c ,\ 7 vec a-8 vec b+9 vec c\ a n d\ 3 vec a+20 vec b+5 vec c

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.

If a ,\ b ,\ c are non coplanar vectors prove that the points having the following position vectors are collinear: vec a ,\ vec b ,\ 3 vec a-2 vec b

If a ,\ b ,\ c are non coplanar vectors prove that the points having the following position vectors are collinear: vec a+ vec b+ vec c ,\ 4 vec a+3 vec b ,\ 10 vec a+7 vec b-2 vec c

Prove that [ vec a , vec b , vec c+ vec d]=[ vec a , vec b , vec c]+[ vec a , vec b , vec d]

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

If vec a , vec b , vec c are three non-coplanar vectors, prove that [ vec a+ vec b+ vec c vec a+ vec b vec a+ vec c]=-[ vec a vec b vec c]

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prove that: vec a-2 vec b+3 vec c ,-2 vec a+3 vec b-4 vec ca n d vec c-3 vec b+5 vec c are coplanar 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.