S.T the points whose P.V are `bar(a) - 2bar(b) + 3bar(c ), 2bar(a)+3bar(b)-4bar(c ), -7bar(b)+10bar(c )` are collinear.

Show that the points whose P,V are -2bar(a)+3bar(b)+5bar(c ), bar(a)+2bar(b)+3bar(c ) , 7bar(a)-bar(c ) are collinear, where bar(a),bar(b), bar(c ) are non-coplanar vectors.

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)

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

The points with P.V's bar(i)+2bar(j)+bar(k), 2bar(i)+3bar(j)+4bar(k) and 4bar(i)+5bar(j)+10bar(k) form

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