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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryFamily of planesMedium2 minQB

MathematicsMediumsingle choice

Find the $x$ -intercept of the plane through the intersection of $x + 2 y + 3 z + 5 = 0$ and $2 x - 3 y + 7 z + 1 = 0$ , parallel to $r = \hat{i} + 2 \hat{j} + t (8 \hat{i} - 7 \hat{j} - 4 \hat{k})$ .

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Answer:

Solution:

A plane in the pencil has normal $(1 + 2 s, 2 - 3 s, 3 + 7 s)$ . Perpendicularity to $(8, - 7, - 4)$ gives $s = 2$ , and the intercept is $- (5 + s) / (1 + 2 s) = - 7/5$ .

Stream:JEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Family of planes

⏱ 2mℹ️ Source: QB

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