Question

Two planes $a_1x + b_1y + c_1z + d_1 = 0$ and $a_2x + b_2y + c_2z + d_2 = 0$ are parallel if :

• A. $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
• B. $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
• C. $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
• D. $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Answer 1

Answer: (A)

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Answer 2

We know that two planes $a_1 x + b_1 y + c_1 z + d_1 = 0$ and $a_2x + b_2y + c_2z + d_2 = 0$ are parallel if $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} .$