Show that the four points `A ,B , Ca n dD` with position vectors ` vec a , vec b , vec c` and ` vec d` respectively are coplanar if and only if `3 vec a-2 vec b+ vec c-2 vec d=0.`

Prove that the points A ,Ba n d C with position vectors vec a , vec ba n d vec c respectively are collinear if and only if vec axx vec b+ vec bxx vec c+ vec cxx vec a= vec0dot

Show that the four points A ,B ,C ,D with position vectors vec a , vec b , vec c , vec d respectively such that 3 vec a-2 vec b+5 vec c-6 vec d= vec0 , are coplanar. Also, find the position vector of the point of intersection of the line segments A C and B Ddot

Show that the points A ,B ,C with position vectors -2 vec a+3 vec b+5 vec c , vec a+2 vec b+3 vec c a n d7 vec a- vec c respectively, are collinear.

Show that the point A ,B ,C with position vectors vec a-2 vec b+3 vec c ,2 vec a+3 vec b-4 vec c and -7 vec b+10 vec c are collinear.

Show that the point A ,B ,C with position vectors vec a-2 vec b+3 vec c ,2 vec a+3 vec b-4 vec c and -7 vec b+10 vec c are collinear.

Show that the points with position vectors vec a-2 vec b+3 vec c ,\ -2 vec a+3 vec b- vec c\ a n d\ 4 vec a-7 vec b+7 vec c are collinear.

Show that the vectors vec a , vec b and vec c are coplanar if vec a+ vec b , vec b+ vec c and vec c+ vec a are coplanar.

Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a are coplanar.

Show that the points with position vectors vec a-2 vec b+3 vec c ,-2 vec a+3 vec b+2 vec ca n d-8 vec a+13 vec b are collinear whatever be vec a , vec b , vec cdot

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vecd dot vec a= vecd dot vec b= vec d dot vec ca n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these