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Three Dimensional Geometry — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSThree Dimensional Geometry1 Mark
MCQ
$l = m = n = 1$ represents the direction cosines of:
  • A
    $x−$axis
  • B
    $y−$axis
  • C
    $z−$axis
  • ✓
    none of these
✓

Answer

Correct option: D.
none of these
Suppose, $\text{l, m, n}$ are direction cosines
$\Rightarrow 1^2 + m^2 + n^2 = 1$
But $ 1 = m = n = 1$
$\Rightarrow 3m^2 = 1$
$\Rightarrow 1 = m = n = \frac{1}{\sqrt3}$​
which are not direction cosines of either of the three co$-$ordinate axes.

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