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If vec xa n d vec y are two non-colline...

If ` vec xa n d vec y` are two non-collinear vectors and a, b, and c represent the sides of a ` A B C` satisfying `(a-b) vec x+(b-c) vec y+(c-a)( vec x X vec y)=0,` then ` A B C` is (where ` vec x X vec y` is perpendicular to the plane of `xa n dy` ) a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. a scalene triangle

A

an acute angled triangle

B

ann obtuse angled triangle

C

a right angled triangle

D

a scalene triangle

Text Solution

Verified by Experts

The correct Answer is:
A
As x,y and `x xxy` 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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