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Let a,b,c denote the lengths of the side...

Let a,b,c denote the lengths of the sides of a triangle such that
` ( a-b) vecu + ( b-c) vecv + ( c-a) (vecu xx vecv) = vec0`
For any two non-collinear vectors ` vecu and vecu`,then the triangle is

A

right angled

B

equilateral

C

isoscels

D

obtuse angled

Text Solution

Verified by Experts

The correct Answer is:
B
Since, ` vecu , vecv and vecu xx vecv` , are non- coplanar vectors.
` (a -b) vecu + ( b -c) vecu + ( c-a) ( vecu xx vecv) = vec0`
` Rightarrow a-b=0=b -c =c -a`
` Rightarrow a-b =0=b -c = c-a`
` Rightarrow a=l=c `
` Rightarrow ` Triangle is equilateral.
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