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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 ?

A

P_{1}

and

P_{3}

are parallel.

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B

P_{2}

and

P_{3}

are parallel.

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C

P_{1}

and

P_{2}

are parallel.

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D

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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Similar questions

Q. Consider the three planes

P_{1} : 3 x + 15 y + 21 z = 9

P_{2} : x - 3 y - z = 5,

P_{3} : 2 x + 10 y + 14 z = 5

Then, which one of the following is true ?

Q. Consider three planes

P_{1} : x - y + z = 1

P_{2} : x + y - z = - 1

P_{3} : x - 3 y + 3 z = 2

L_{1}, L_{2}, L_{3}

be the lines of intersection of the planes

P_{2}

P_{3}, P_{3}

P_{1}

P_{1}

P_{2}

, respectively.
STATEMENT-

1

: At least two of the lines

L_{1}, L_{2}

L_{3}

are non-parallel.
and
STATEMENT -

2

: The three planes do not have a common point.

Q. Consider the planes

P_{1} : c y + b z = x

P_{2} : a z + c x = y

P_{3} : b x + a y = z .

P_{1}, P_{2}

P_{3}

pass through one line, if

Consider three planes:

P_{1} : x - y + z = 1 P_{2} : x + y - z = 1 P_{3} : x - 3 y + 3 z = 2

L_{1}, L_{2}, L_{3}

be the lines of intersection of the planes

P_{2}

P_{3}, P_{3}

P_{1}, P_{1}

P_{2},

At least two of the lines

L_{1}, L_{2}

L_{3}

are non-parallel. Reason: The three planes do not have a common point.

R^{3}

, consider the planes

P_{1} : y = 0

P_{2} : x + z = 1

P_{3}

be a plane, different from

P_{1}

P_{2}

, which passes through the intersection of

P_{1}

P_{2}

. If the distance of the point

(0, 1, 0)

P_{3}

1

and the distance of a point

(α, β, γ)

P_{3}

2

, then which of the following relations is (are) true?

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Equation of a Plane : General Form

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