Consider the three planes P 1- 3 x -15 y -21 z -9P 2- x -3 y - z -5- andP 3- 2 x -10 y -14 z -5Then- which one of the following is true-A- P 1 and P 3 are parallel-B- P 2 and P 3 are parallel-C- P 1- P 2 and P 3 all are parallel-D- P 1 and P 2 are parallel-

P_1:x+5y+7z=3 P_2:x 3y z=5 P_3:x+5y+7z=52 ⇒ P_1∥ P_3 ...

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Byju's Answer

Standard XII

Mathematics

Equation of a Plane : General Form

Consider the ...

Question

Consider the three planes
$P_{1} : 3 x + 15 y + 21 z = 9$
$P_{2} : x - 3 y - z = 5,$ and
$P_{3} : 2 x + 10 y + 14 z = 5$
Then, which one of the following is true ?

P_{1}

and

P_{3}

are parallel.

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P_{2}

and

P_{3}

are parallel.

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P_{1}

and

P_{2}

are parallel.

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P_{1}, P_{2}

and

P_{3}

all are parallel.

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Solution

The correct option is A $P_{1}$ and $P_{3}$ are parallel.
$P_{1} : x + 5 y + 7 z = 3$
$P_{2} : x - 3 y - z = 5$
$P_{3} : x + 5 y + 7 z = \frac{5}{2}$
$\Rightarrow P_{1} ∥ P_{3}$

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Consider the three planes P1:3x+15y+21z=9 P2:x−3y−z=5, and P3:2x+10y+14z=5 Then, which one of the following is true ?

The correct option is A P1 and P3 are parallel.P1:x+5y+7z=3 P2:x−3y−z=5 P3:x+5y+7z=52 ⇒P1∥P3

Consider the three planes
$P_{1} : 3 x + 15 y + 21 z = 9$
$P_{2} : x - 3 y - z = 5,$ and
$P_{3} : 2 x + 10 y + 14 z = 5$
Then, which one of the following is true ?

The correct option is A $P_{1}$ and $P_{3}$ are parallel.
$P_{1} : x + 5 y + 7 z = 3$
$P_{2} : x - 3 y - z = 5$
$P_{3} : x + 5 y + 7 z = \frac{5}{2}$
$\Rightarrow P_{1} ∥ P_{3}$