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$If \vec{x} and \vec{y} are two non-collinear vectors and a, b, c represent the sides of a$ $△ A B C satisfying (a - b) \vec{x} + (b - c) \vec{y} + (c - a) (\vec{x} \times \vec{y}) = 0, then Δ A B C is:$

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Correct option is A

As x→,y→ and x→×y→ are non-coplanar vectors ⇒ linearly independent. Therefore, a−b=0=b−c=c−a⇒ a=b=c⇒Δ is equilateral.

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If x→ and y→ are two non-collinear vectors and a,b,c represent the sides of a △ABC satisfying (a−b)x→+(b−c)y→+(c−a)(x→×y→)=0, then ΔABC is:

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Ready to Test Your Skills?

free study material

$If \vec{x} and \vec{y} are two non-collinear vectors and a, b, c represent the sides of a$ $△ A B C satisfying (a - b) \vec{x} + (b - c) \vec{y} + (c - a) (\vec{x} \times \vec{y}) = 0, then Δ A B C is:$