If A = ( − 2 , 2 , 3 ) , B = ( 3 , 2 , 2 ) , C = ( 4 , − 3 , 5 ) and D = ( 7 , − 5 , − 1 ) Then the projection of AB on CD is

A = ( − 2 , 2 , 3 ) ; B = ( 3 , 2 , 2 ) ; C = ( 4 , − 3 , 5 ) and D = ( 7 , − 5 , − 1 ) AB = 5 i ^ − k ^ and CD = 3 i ^ − 2 j ^ − 6 k ^ Projection of AB on CD = ∣ CD ∣ AB ⋅ CD = ( 3 ) 2 + ( − 2 ) 2 + ( − 6 ) 2 ( 5 i ^ − k ^ ) ⋅ ( 3 i ^ − 2 j ^ − 6 k ^ ) = 7 15 + 6 = 3

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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2021

MathematicsEasysingle choice

If $A = (- 2, 2, 3), B = (3, 2, 2), C = (4, - 3, 5)$ and $D = (7, - 5, - 1)$ Then the projection of $\overline{AB}$ on $\overline{CD}$ is

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Answer:

Solution:

$A = (- 2, 2, 3); B = (3, 2, 2); C = (4, - 3, 5) and D = (7, - 5, - 1) \overline{AB} = 5 \hat{i} - \hat{k} and \overline{CD} = 3 \hat{i} - 2 \hat{j} - 6 \hat{k} Projection of \overline{AB} on \overline{CD} = \frac{AB \cdot CD}{∣ CD ∣} = \frac{( 5 i ^ - k ^ ) \cdot ( 3 i ^ - 2 j ^ - 6 k ^ )}{( 3 ) ^{2} + ( - 2 ) ^{2} + ( - 6 ) ^{2}} = \frac{15 + 6}{7} = 3$

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

⏱ 2mℹ️ Source: PYQ_2021

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