" 12.Show that points "2bar(a)+3vec b-bar(c),bar(a)-2bar(b)+3bar(c),quad 3bar(a)+4bar(b)-2bar(c),bar(a)-6bar(b)+6bar(c)" are coplanar."

If bar(a),bar(b),bar(c) are non-coplanar vectors.Prove that the four points -bar(a)+4bar(b)-3bar(c) , 3bar(a)+2bar(b)-5bar(c) , -3bar(a)+8bar(b)-5bar(c) , -3bar(a)+2bar(b)+bar(c) are coplanar.

The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5bar(c) are

Show that points with p.v bar(a)-2bar(b)+3bar(c ),-2bar(a)+3bar(b)-bar(c ),4bar(a)-7bar(b)+7bar(c ) are collinear. It is given that vectors bara,barb,bar c are non-coplanar.

Show that points with p.v bar(a)-2bar(b)+3bar(c ),-2bar(a)+3bar(b)-bar(c ),4bar(a)-7bar(b)+7bar(c ) are collinear. It is given that vectors bara,barb,bar c are non-coplanar.

Find a linear relation between the vectors bar(a)+3bar(b)+4bar(c), bar(a)-2bar(b)+3bar(c), bar(a)+5bar(b)-2bar(c) and 6bar(a)+14bar(b)+4bar(c)" where "bar(a), bar(b), bar(c) are non coplanar vectors.

Show that the following vectors are linearly dependent bar(a)-2bar(b)+bar(c), 2bar(a)+bar(b)-bar(c), 7bar(a)-4bar(b)+bar(c) where bar(a), bar(b), bar(c) are non-coplanar vectors

(bar(a)+2bar(b)-bar(c))*(bar(a)-bar(b))xx(bar(a)-bar(bar(c)))=

Prove that the following four points are coplanar. i) 4bar(i)+5bar(j)+bar(k), -bar(j)-bar(k), 3bar(i)+9bar(j)+4bar(k), -4bar(i)+4bar(j)+4bar(k) ii) -bar(a)+4bar(b)-3bar(c), 3bar(a)+2bar(b)-5bar(c), -3bar(a)+8bar(b)-5bar(c), -3bar(a)+2bar(b)+bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors) iii) 6bar(a)+2bar(b)-bar(c), 2bar(a)-bar(b)+3bar(c), -bar(a)+2bar(b)-4bar(c), -12bar(a)-bar(b)-3bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors)