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Three Dimensional Geometry
NCERT Class 12
CBSE
Grade 12
Question:
The direction cosines of a line which is equally inclined to the coordinate axes are: (a) $\pm \left(\dfrac{1}{\sqrt{3}}, \dfrac{1}{\sqrt{3}}, \dfrac{1}{\sqrt{3}}\right)$ (b) $\pm \left(\dfrac{1}{3}, \dfrac{1}{3}, \dfrac{1}{3}\right)$ (c) $\pm (1, 1, 1)$ (d) $\pm \left(\dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}\right)$
Step-by-Step Solution
3l^2 = 1 \Rightarrow l = m = n = \pm 1/\sqrt{3}. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Selecting $\pm(1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3})$: 1.0 Mark