Question

In a three-dimensional space, the equation $3x-4y=0$ represents.

• A. A plane containing $Z-axis$
• B. A plane containing $X-axis$
• C. A plane containing $Y-axis$
• D. Passing through $(0,0)$

Answer 1

The correct option is A A plane containing $Z-axis$

If we consider the z-part also, then the equation is $3x-4y+0z=0$

Which means on putting any value of z equation will have no effect as $0\times z=0$

$\therefore$ it will be a plane containing $Z-axis$.($\because$ it will pass through all points z if it satisfy condition for$(x,y)$)

(D) is not right because its plane and not a line so it will pass through $(0,0,0)$ not $(0,0)$.

Hence, $\left(A\right)$