If the plane 3 x + y + 2 z + 6 = 0 is parallel to the line 2 b 3 x − 1 = 3 − y = a z − 1 , then the value of 3 a + 3 b is

Given plane 3 x + y + 2 z + 6 = 0 and line 3 2 b x − 3 1 = − 1 y − 3 = a z − 1 Since, plane is parallel to line, then 3 ( 3 2 b ) + ( 1 ) ( − 1 ) + 2 ( a ) = 0 2 b − 1 + 2 a = 0 ⇒ a + b = 2 1 Now, 3 a + 3 b = 2 3

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Mathematics3D-Coordinate GeometryMiscellaneous/MixedMedium2 minPYQ_2022

MathematicsMediumsingle choice

If the plane $3 x + y + 2 z + 6 = 0$ is parallel to the line $\frac{3 x - 1}{2 b} = 3 - y = \frac{z - 1}{a}$ , then the value of $3 a + 3 b$ is

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Given plane $3 x + y + 2 z + 6 = 0$ and line $\frac{x - \frac{1}{3}}{\frac{2 b}{3}} = \frac{y - 3}{- 1} = \frac{z - 1}{a}$ Since, plane is parallel to line, then $3 (\frac{2 b}{3}) + (1) (- 1) + 2 (a) = 0 2 b - 1 + 2 a = 0 \Rightarrow a + b = \frac{1}{2}$ Now, $3 a + 3 b = \frac{3}{2}$

Stream:BITSATSubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2022

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