Question

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

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

Answer 1

The correct option is D an isosceles triangle

Given

$(20a-15b)\overrightarrow{x}+(15b-20c)\overrightarrow{y}+(12c-20a)(\overrightarrow{x}\times \overrightarrow{y})$

Since $\overrightarrow{x}$ & $\overrightarrow{y}$ are two non-collinear vector

Hence,

$20a-15b=0,15b-20c=0$

$20a=15b$

$15b=20c$

$\therefore 20a=20c$

$\therefore a=c$

Hence, Triangle is isosceles triangle