`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)`

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 ) .

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)

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) = 2bar(i) - 3bar(j) + bar(k) and bar(b) = bar(i) + 4bar(j) -2bar(k) , then find (bar(a) + bar(b))xx(bar(a)-bar(b))

Compute bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + bar(c ) xx (bar(a)+bar(b))