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Q.

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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a

an acute angle triangle

b

an obtuse angle triangle

c

a right angle triangle

d

a scalene triangle

answer is A.

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Detailed Solution

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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