i) If `bar(a), bar(b), bar(c)` are non coplanar vectors, then prove that the vectors `5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c)` are coplanar.

If bar(a), bar(b), bar(c) are non coplanar, show that the vectors bar(a)+2bar(b)-bar(c), 2bar(a)-3bar(b)+2bar(c), 4bar(a)+bar(b)+3bar(c) are linearly independent.

If bar(a), bar(b), bar(c) are non coplanar then the vectors bar(a)-2bar(b)+3bar(c), -2bar(a)+3bar(b)-4bar(c), bar(a)-3bar(b)+5bar(c) are

If bar(a), bar(b), bar(c) are non coplanar vectors and lambda is a real number, then the vectors bar(a)+2bar(b)+3bar(c), lambdabar(b)+4bar(c) and (2lambda-1)bar(c) are non-coplanar for

If bar(a), bar(b), bar(c) are linearly independent vectors, then show that bar(a)-3bar(b)+2bar(c), 2bar(a)-4bar(b)-bar(c), 3bar(a)+2bar(b)-bar(c) are linearly independent.

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

If bar(a), bar(b), bar(c) are three non-coplanar vectors, then the vector equation bar(r)=(1-p-q)bar(a)+pbar(b)+qbar(c) represents

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 ) .

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)