VectorHard

Question

If the vectors non-coplanar and l, m, n are distinct real numbers, then = 0 implies -

Options

A.lm + mn + nl = 0
B.l + m + n = 0
C.l2 + m2 + n2 = 0
D.l3 + m3 + n3 = 0

Solution

= 0
Let
= (l2 - mn) (n2 - lm) + (m2 - ln)
Now
⇒ [abc] (l3 - lmn + m3 - lmn + n3 - lmn) = 0
⇒ [abc] (l3 + m3 + n3 - 3l mn) = 0
⇒ l + m + n = 0.

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