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Let {P}_{{1}}:{2}{x}+{y}-{z}={3}and {P}_{{2}}:{x}+{2}{y}+{z}={

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Let $P_{1} : 2 x + y - z = 3$ and $P_{2} : x + 2 y + z = 2$ be two planes. Then, which of the following statement(s) is (are) TRUE?The line of intersection of $P_{1}$ and $P_{2}$ has direction ratios $1, 2, - 1$ (b) The line $\frac{3 x - 4}{9} = \frac{1 - 3 y}{9} = \frac{z}{3}$ is perpendicular to the line of intersection of $P_{1}$ and $P_{2}$ (c) The acute angle between $P_{1}$ and $P_{2}$ is $60 o$ (d) If $P_{3}$ is the plane passing through the point $(4, 2, - 2)$ and perpendicular to the line of intersection of $P_{1}$ and $P_{2}$ , then the distance of the point $(2, 1, 1)$ from the plane $P_{3}$ is $\frac{2}{3}$

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Amelia Discussed

Let

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

and

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

be two planes. Then, which of the following statement(s) is (are) TRUE?The line of intersection of

P_{1}

and

P_{2}

has direction ratios

1, 2, - 1

(b) The line

\frac{3 x - 4}{9} = \frac{1 - 3 y}{9} = \frac{z}{3}

is perpendicular to the line of intersection of

P_{1}

and

P_{2}

P_{1}

and

P_{2}

60 o

(d) If

P_{3}

is the plane passing through the point

(4, 2, - 2)

and perpendicular to the line of intersection of

P_{1}

and

P_{2}

, then the distance of the point

(2, 1, 1)

from the plane

P_{3}

\frac{2}{3}

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Question Text	Let $P_{1} : 2 x + y - z = 3$ and $P_{2} : x + 2 y + z = 2$ be two planes. Then, which of the following statement(s) is (are) TRUE?The line of intersection of $P_{1}$ and $P_{2}$ has direction ratios $1, 2, - 1$ (b) The line $\frac{3 x - 4}{9} = \frac{1 - 3 y}{9} = \frac{z}{3}$ is perpendicular to the line of intersection of $P_{1}$ and $P_{2}$ (c) The acute angle between $P_{1}$ and $P_{2}$ is $60 o$ (d) If $P_{3}$ is the plane passing through the point $(4, 2, - 2)$ and perpendicular to the line of intersection of $P_{1}$ and $P_{2}$ , then the distance of the point $(2, 1, 1)$ from the plane $P_{3}$ is $\frac{2}{3}$
Answer Type	Video solution: 1
Upvotes	150

Filo tutor solutions (1)

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