Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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

MathematicsEasysingle choice

A line makes an angle of $4 5^{\circ}$ with $x$ -axis and congruent angles with $y$ and $z$ -axes, then the direction cosines of the line are

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Solution:

Let angle made by line with each of $X$ and $Z$ axis be $θ$ . $∴ cos^{2} 4 5^{\circ} + cos^{2} θ + cos^{2} θ = 1$ $2 cos^{2} θ = 1 - \frac{1}{2} = \frac{1}{2} \Rightarrow cos^{2} θ = \frac{1}{4} \Rightarrow cos θ = \pm \frac{1}{2}$ Hence d.r.s. are $\frac{1}{2}, \frac{1}{2}, \frac{1}{2}$ or $\frac{1}{2}, \frac{- 1}{2}, \frac{- 1}{2}$

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

⏱ 2mℹ️ Source: PYQ_2020

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