Let $ heta_1$ be the angle between two lines $2 x+3 y+$ $c_1=0$ and $-x+5 y+c_2=0$ and $ heta_2$ be the angle between two lines $2 x+3 y+c_1=0$ and $-x+5 y+$ $c_3=0$, where $c_1, c_2, c_3$ are any real numbers : Statement-1: If $c_2$ and $c_3$ are proportional, then $ heta_1= heta_2$.…

Question

Let $	heta_1$ be the angle between two lines $2 x+3 y+$ $c_1=0$ and $-x+5 y+c_2=0$ and $	heta_2$ be the angle between two lines $2 x+3 y+c_1=0$ and $-x+5 y+$ $c_3=0$, where $c_1, c_2, c_3$ are any real numbers : Statement-1: If $c_2$ and $c_3$ are proportional, then $	heta_1=	heta_2$. Statement-2: $	heta_1=	heta_2$ for all $c_2$ and $c_3$.

Aicharya · Accepted Answer

Two lines $-x+5 y+c_2=0$ and $-x+5 y+c_3$ $=0$ are parallel to each other. Hence statement-1 is true, statement-2 is true and statement-2 is the correct explanation of statement-1.

Let $\theta_1$ be the angle between two lines $2 x+3 y+$ $c_1=0$ and $-x+5 y+c_2=0$ and $\theta_2$ be the…

Solution