Browse Questions

# If the directions cosines of a line are $k,k,k$ then

$(A)\;k\;>\;0\qquad(B)\;0\;<\;k\;<\;1\qquad(C)\;k\;=\;1\qquad(D)\;k\;=\;\frac{1}{\sqrt 3} or \frac{-1}{\sqrt 3}$

Toolbox:
• The sum of the squares of direction cosines is one.$(ie) \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1$
Given that the direction cosines of a line are $k,k,k$
The value of $k$ is $\pm \large\frac{1}{\sqrt 3}$
We know the sum of the squares of the direction cosines is one.
$(ie) k^2+k^2+k^2=1$
$=>3k^2=1$
$=>k^2=\large\frac{1}{3}$
$k=\pm \large\frac{1}{\sqrt 3}$
Hence the correct option is $D$