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Q.

If x and y are two non-collinear vectors and a, b and c represent the sides of a ABC satisfying (a-b)x+(b-c)y+(c-a)(x×y)=0, then ABC is (where x × y is perpendicular to the plane of x and y)

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a

a right angled triangle

b

an acute angled triangle

c

an obtuse angled triangle

d

a scalene triangle

answer is A.

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Detailed Solution

As x, y and  x × y are non-collinear vectors, vectors are linearly independent.
Hence,

a-b=0=b-c=c-a
or        a=b=c

Therefore, the triangle is equilateral.

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