Question

If $\overline{a},\overline{b}$ are two non collinear and non zero vectors such that $(x-y)(\overline{a}\times \overline{b})+(y-z)\overline{a}+(z-x)\overline{b}=\overline{0}$ where x, y, z are the lengths of the sides of a triangle, then the triangle is

• A. right angled
• B. isosceles
• C. equilateral
• D. none

Answer 1

The correct option is C

equilateral

$\overline{a},\overline{b},\overline{a}\times \overline{b}$ are non coplanar

$\Rightarrow$x – y = 0, y – z = 0, z – x = 0 $\Rightarrow$ x = y = z