If a line makes angles of measure 6 π and 3 π with X and Y axes respectively, then the angle made by the line with Z axis is

Let the line make an angle θ with Z axis. ∴ cos 2 6 π + cos 2 3 π + cos 2 θ = 1 ∴ cos 2 θ = 1 − ( 4 3 + 4 1 ) = 0 ⇒ θ = 2 π

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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2020

MathematicsEasysingle choice

If a line makes angles of measure $\frac{π}{6}$ and $\frac{π}{3}$ with $X$ and Y axes respectively, then the angle made by the line with $Z$ axis is

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Solution:

Let the line make an angle $θ$ with $Z$ axis. $∴ cos^{2} \frac{π}{6} + cos^{2} \frac{π}{3} + cos^{2} θ = 1 ∴ cos^{2} θ = 1 - (\frac{3}{4} + \frac{1}{4}) = 0 \Rightarrow θ = \frac{π}{2}$

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

⏱ 2mℹ️ Source: PYQ_2020

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