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Dot Product

If p, q are t...

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 triangle, then the triangle is:

A

Right angled

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B

Obtuse angled

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C

Equilateral

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D

Isosceles

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Solution

The correct option is C Equilateral
$\to p \times \to q$ is perpendicular to both $\to p$ and $\to q$ . Hence $\to p$ , $\to q$ and $\to p \times \to q$ are non coplanar.
$∴ (b - c) \to p \times \to q + (c - a) \to p + (a - b) \to q = 0$
$\Rightarrow b - c = c - a = a - b = 0 \Rightarrow a = b = c$
Hence triangle is equilateral.

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