The equations of two given planes are
$a_{1} x + b_{1} y + c_{1} z = d_{1} a_{2} x + b_{2} y + c_{2} z = d_{2}$
If both the planes are parallel then which of the following is true:

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

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

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\frac{a_{2}}{a_{1}} = \frac{b_{2}}{b_{1}} = \frac{c_{2}}{c_{1}} \neq \frac{d_{2}}{d_{1}}

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None of the above

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Solution

The correct option is C $\frac{a_{2}}{a_{1}} = \frac{b_{2}}{b_{1}} = \frac{c_{2}}{c_{1}} \neq \frac{d_{2}}{d_{1}}$
For parallel planes, the equations must satisfy the given condition $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \neq \frac{d_{1}}{d_{2}}$

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Similar questions

a_{1} x + b_{1} y + c_{1} z = d_{1} a_{2} x + b_{2} y + c_{2} z = d_{2}

a_{1} x + b_{1} y + c_{1} z + d_{1} = 0

a_{2} x + b_{2} y + c_{2} z + d_{2} = 0

A = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & a_{3} \end{matrix} ∣ ∣ ∣ ∣ \neq 0,

a_{1} x + b_{1} y + c_{1} z = 0, a_{2} x + b_{2} y + c_{2} z = 0

a_{3} x + b_{3} y + c_{3} z = 0

a_{1} x + b_{1} y + c_{1} z = 0

a_{2} x + b_{2} y + c_{2} z = 0

a_{3} x + b_{3} y + c_{3} z = 0

i f ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{3} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = 0,

a_{1} x + b_{1} y + c_{1} z = 0 . . . (1),

a_{2} x + b_{2} y + c_{2} z = 0 . . . (2),

a_{3} x + b_{3} y + c_{3} z = 0 . . . (3)

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