Question

If $\overrightarrow{x}$ and $\overrightarrow{y}$ are two non-collinear vectors and $ABC$ is a triangle with sides $a,b,c$ satisfying $(20a-15b)\overrightarrow{x}+(15b-12c)\overrightarrow{y}+(12c-20a)$ $(\overrightarrow{x}\times \overrightarrow{y})=\overrightarrow{0}$, then the triangle $ABC$ is

• A. An acute angle triangle
• B. An obtuse angle triangle
• C. A right angle triangle
• D. An isosceles triangle

Answer 1

The correct option is C A right angle triangle

$(20a-15b)\overrightarrow{x}+(15b-12c)\overrightarrow{y}+(12c-20a)\overrightarrow{x}\times \overrightarrow{y}=0$
So as they are not collinear than
$20a=15b$ ___________(1)
$15b=12c$ __________(2)
$12c=20a$ ___________(3)
$a=3$ $b=4$ $c=5$
$c^2=a^2+b^2$