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kkurt [141]
3 years ago
15

Show that (×)× = ×(×) if and only if the vectors and are collinear.

Mathematics
1 answer:
WITCHER [35]3 years ago
3 0

Step-by-step explanation:

<em>NOTE: Bolded letters are vectors</em>

Given that ,

  • (axb)xc = ax(bxc)

From vector triple product rule,

  • ax(bxc) = b(a.c)-c(a.b)
  • ax(bxc) = b(a.c)-a(b.c)

If these both are equal, then :

⇒b(a.c)-c(a.b) = b(a.c)-a(b.c)

⇒(-a.b)c = (-b.c)a

⇒(|a||b|sin∅)c = (|b||c|sinФ)a (cancel |b| on both sides)

A , C are the unit vectors of a and c respectively .

Two vectors can be equal on when their magnitude and directions are same.

That is when ,

⇒(|a||c|sin∅)A = (|a||c|sinФ)C

⇒sin∅A = sinФC

This can only be possible when the vectors are collinear because the angle made by the vectors with the vector B should be the same or supplementary and the vectors A and C must be in the same direction.

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