If p- q- are two non collinear and non zero vectors such that b-c p-q- c-a p- a-b q-0 where a- b- c are the lengths of the sides of a triangle- then the triangle is

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Standard XII

Physics

Vector Component

If p⃗, q⃗ a...

Question

If $\to p, \to q$ are two non collinear and non zero vectors such that $(b - c) \to p \times \to q + (c - a) \to p + (a - b) \to q = 0$ where a, b, c are the lengths of the sides of a triangle, then the triangle is

Right angled

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Obtuse angled

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Equilateral

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Isosceles

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Solution

The correct option is C Equilateral
Given $p$ and $q$ are non collinear and non zero vectors
Given $(b - c) (p \times q) + (c - a) p + (a - b) q = 0$
Since $p$ and $q$ are non zero and non collinear vectors , $p \times q$ is also a non zero vector
Therefore for the given equation to be true $b - c = 0$ , $c - a = 0$ and $a - b = 0$
$\Rightarrow a = b = c$
Therefore $a, b, c$ represents lengths of equilateral triangle
Therefore the correct option is $C$

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