If p-q- are two noncollinear and nonzero vectors such that b - cp-q- - c - ap- - a - bq- - 0-where a-b-c are the length of the sides of a triangle - then the triangle is

The correct option is D isocelesConsider the problem #160; p⃗×q⃗ is any vector perpendicular to both p⃗ and q⃗ .So, p⃗,q⃗ and p⃗×q ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

If p⃗,q⃗ ar...

Question

If $\to p, \to q$ are two noncollinear and nonzero 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 length 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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isoceles

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Solution

The correct option is D isoceles
Consider the problem

$\to p \times \to q$ is any vector perpendicular to both $\to p$ and $\to q$ .
So, $\to p, \to q$ and $\to p \times \to q$ are non planar.
Hence,
the given relation is possible when
$b - c \neq 0, c - a = 0$ and $a - b \neq 0$
i.e. a=c
Hence it is isosceles.

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Similar questions

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(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

Q. If

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If →p,→q are two noncollinear and nonzero vectors such that (b−c)→p×→q+(c−a)→p+(a−b)→q=0,where a,b,c are the length of the sides of a triangle , then the triangle is

The correct option is D isocelesConsider the problem →p×→q is any vector perpendicular to both →p and →q.So, →p,→q and →p×→q are non planar.Hence, the given relation is possible when b−c≠0,c−a=0 and a−b≠0i.e. a=cHence it is isosceles.

If $\to p, \to q$ are two noncollinear and nonzero 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 length of the sides of a triangle , then the triangle is