Question
If the direction cosines of a line are $k$, $k$ and $k$, then
- (a) $k > 0$
- (b) $0 < k < 1$
- (c) $k = 1$
- (d) $k = \frac{1}{{\sqrt 3 }}$ or $- \frac{1}{{\sqrt 3 }}$ ✓ Correct
Three Dimensional Geometry — Class 12 Maths Solution
Step-by-step Solution
Since, direction cosines of a line are $k$, $k$ and $k$.
$\therefore$ $l = k,m = k$ and $n = k$
As we know, ${l^2} + {m^2} + {n^2} = 1$
$\Rightarrow$ ${k^2} + {k^2} + {k^2} = 1$
$\Rightarrow$ ${k^2} = \frac{1}{3}$
$\therefore k = \pm \frac{1}{{\sqrt 3 }}$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Three Dimensional Geometry. Curated by Sachin Sharma. Free for all students.