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Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minPYQ_2020

MathematicsMediumnumerical

The projection of the line segment joining the point $(1, - 1, 3)$ and $(2, - 4, 11)$ on the line joining the points $(- 1, 2, 3)$ and $(3, - 2,10)$ is _______

Answer:

8.00

Solution:

Let A $(1, - 1,3)$ , B $(2, - 4, 11)$
$\vec{A B} = \hat{i} - 3 \hat{j} + 8 \hat{k}$
C $(- 1, 2, 3)$ , D $(3, - 2, 10)$
$\vec{C D} = 4 \hat{i} - 4 \hat{j} + 7 \hat{k}$
Projection of $\vec{A B}$ on $\vec{C D}$ $= \frac{\vec{A B} . \vec{C D}}{|\vec{C D}|} = (\frac{4 + 12 + 56}{\sqrt{16 + 16 + 49}}) = \frac{72}{9} = 8$

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

⏱ 2mℹ️ Source: PYQ_2020

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