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Q.

If  x→ and y→ are two non-collinear vectors and, ABC is a triangle with side lengths a ,b and c satisfying  (20a−15b)x→+(15b−12c)y→+(12c−20a)(x→×y→)=0→  Then triangle ABC is

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a

an acute-angled triangle

b

an obtuse-angled triangle

c

a right-angled triangle

d

an isosceles triangle

answer is C.

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Detailed Solution

Since x→,y→ and x→×y→  are linearly independent, we have  20a−15b=15b−12c=12c−20a=0⇒ a3=b4=c5⇒ c2=a2+b2Hence, ∆ABC is right angled.
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