If 2z1-3z2-z3=0 , then z1,z2,z3 are represented by

Question

If 2z1-3z2-z3=0 , then z1,z2,z3 are represented by (A) three vertices of a triangle (B) three collinear points (C) three vertices of a rhombus (D) none of these

Tardigrade Admin · Accepted Answer

Since z2=(2z1+z3/2+1) ∴ z2 divides the line joining z1, z3 in the ratio 2: 1 internally. ∴ z1, z2, z3 are collinear.

Q. If $2 z_{1} - 3 z_{2} - z_{3} = 0$ , then $z_{1}, z_{2}, z_{3}$ are represented by

three vertices of a triangle

three collinear points

three vertices of a rhombus

none of these

Since $z_{2} = \frac{2 z _{1} + z _{3}}{2 + 1}$
$∴ z_{2}$ divides the line joining $z_{1}, z_{3}$ in the ratio $2 : 1$ internally.
$∴ z_{1}, z_{2}, z_{3}$ are collinear.

Q. If 2z1​−3z2​−z3​=0 , then z1​,z2​,z3​ are represented by