Question

If $\overset{\rightarrow}{x}$ and $\overset{\rightarrow}{y}$ are two non-collinear vectors and ABC is a triangle with sides a, b, c satisfying (20a – 15b)

$\overset{\rightarrow}{x}$ + (15b – 12c) $\overset{\rightarrow}{y}$ + (12c – 20a) ($\overset{\rightarrow}{x}$ื$\overset{\rightarrow}{y}$) = 0. Then DABC is :

• A. An acute angled
• B. An obtuse angled
• C. A right angled
• D. Isosceles

Answer 1

Answer: (C)

A right angled

Answer 2

$\overset{\rightarrow}{x}$,$\overset{\rightarrow}{y}$ and $\overset{\rightarrow}{x}$×$\overset{\rightarrow}{y}$ are non-coplanar vectors

20a = 15b = 12c

$\frac{a}{3}$= $\frac{b}{4}$ = $\frac{c}{5}$

c² = a² + b²

Hence right angled triangle.