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Prove that the following four points are...

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)

Text Solution

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The correct Answer is:
`bar(PQ),bar(PR),bar(PS)`
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