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Mathematics · JEE | THREE DIMENSIONAL GEOMETRY
हिन्दीGiven below are two statements: Statement I: The vector equation of the line passing through the origin and parallel to the \( x \)-axis is \( \vec{r} = \lambda \hat{i} \). Statement II: The direction cosines of the \( x \)-axis are \( 1, 0, 0 \). In the light of the above statements, choose the most appropriate answer from the options given below:
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Correct answer · Option A
Both Statement I and Statement II are correct.
Explanation
A line along/parallel to the \( x \)-axis passing through origin has direction \( \hat{i} \) and equation \( \vec{r} = \vec{0} + \lambda\hat{i} = \lambda\hat{i} \). The direction cosines of \( x \)-axis are \( \cos 0^\circ, \cos 90^\circ, \cos 90^\circ \) which are \( 1, 0, 0 \). Both statements are correct.
