VectorMedium
Question
If 
are two non collinear vectors and a, b, c represent the sides of aᐃABC satisfying (a - b) 
+ (b - c)
+ (c - a) 
= 0 then ᐃABC is -
are two non collinear vectors and a, b, c represent the sides of aᐃABC satisfying (a - b) + (b - c)
+ (c - a) = 0 then ᐃABC is - Options
A.an acute angle triangle
B.an obtuse angle triangle
C.a right angle triangle
D.a scalene triangle
Solution
(a - b) 
+ (b - c) 
+ (c - a) 
= 0
As
are non zero, non coplanar vectors, then
a - b = b - c = c - a = 0 ⇒ a = b = c
Hence ᐃABC is an equilateral triangle. Hence, acute angled triangle.
+ (b - c) + (c - a) = 0As
are non zero, non coplanar vectors, thena - b = b - c = c - a = 0 ⇒ a = b = c
Hence ᐃABC is an equilateral triangle. Hence, acute angled triangle.
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