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

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.

Show that the following vectors are linearly dependent bar(a)-2bar(b)+3bar(c), -2bar(a)+3bar(b)-4bar(c), -bar(b)+2bar(c)

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

If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the collinearity of the following points whose position vectors are given. i) bar(a)-2bar(b)+3bar(c), 2bar(a)+3bar(b)-4bar(c), -7bar(b)+10bar(c) ii) 3bar(a)-4bar(b)+3bar(c), -4bar(a)+5bar(b)-6bar(c), 4bar(a)-7bar(b)+6bar(c) iii) 2bar(a)+5bar(b)-4bar(c), bar(a)+4bar(b)-3bar(c), 4bar(a)+7bar(b)-6bar(c)

Show that the following vectors are linearly dependent 3bar(a)-2bar(b)-4bar(c), -bar(a)+2bar(c), -2bar(a)+bar(b)+3bar(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)