The acute angle between the line r → = ( i ^ + 2 j ^ + k ^ ) + λ ( i ^ + j ^ + k ^ ) and the plane r → . ( 2 i ^ + j ^ + k ^ ) = 5 is

The angle between the given line and plane is given by sin θ = | ( i ^ + j ^ + k ^ ) . ( 2 i ^ + j ^ + k ^ ) | i ^ + j ^ + k ^ | | 2 i ^ + j ^ + k ^ | | = 4 3 6 = 2 2 3

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

Mathematics3D-Coordinate GeometryMiscellaneous/MixedMedium2 minPYQ_2016

MathematicsMediumsingle choice

The acute angle between the line $\vec{r} = (\hat{i} + 2 \hat{j} + \hat{k}) + λ (\hat{i} + \hat{j} + \hat{k})$ and the plane $\vec{r} . (2 \hat{i} + \hat{j} + \hat{k}) = 5$ is

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Solution:

The angle between the given line and plane is given by
$\sin θ = | \frac{(\hat{i} + \hat{j} + \hat{k}) . (2 \hat{i} + \hat{j} + \hat{k})}{| \hat{i} + \hat{j} + \hat{k} | | 2 \hat{i} + \hat{j} + \hat{k} |} |$
$= \frac{4}{\sqrt{3} \sqrt{6}} = \frac{2 \sqrt{2}}{3}$

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

⏱ 2mℹ️ Source: PYQ_2016

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