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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Hard2 minPYQ_2018

MathematicsHardsingle choice

If points $P (4, 5, x), Q (3, y, 4)$ and $R (5, 8, 0)$ are collinear, then the value of $x + y$ is

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Answer:

Solution:

drs of PQ
$a_{1} = 4 - 3 = 1$
$b_{1} = 5 - y$
$c_{1} = x - 4$
drs of PR
$a_{2} = 5 - 4 = 1$
$b_{2} = 8 - 5 = 3$
$c_{2} = 0 - x = - x$
as P-Q-R collinear
$∴ \frac{1}{1} = \frac{5 - y}{3}$ and $\frac{1}{1} = \frac{x - 4}{- x}$
$∴ 3 = 5 - y and - x = x - 4$
$∴ y = 2 and x = 2$
$∴ x + y =$ $2 + 2 = 4$

Stream:MHT_CETSubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: PYQ_2018

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