Two direction cosines of a line are \(\displaystyle l = \frac{2}{7}\) and \(\displaystyle m = \frac{3}{7}\). If the line makes an obtuse angle with the positive direction of the z-axis, then its third direction cosine n is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle -\frac{6}{7}\)
Direction cosines always satisfy the basic relation \(l^2+m^2+n^2 = 1\):
\( \displaystyle n^2 = 1-\frac{4}{49}-\frac{9}{49} \)
\( \displaystyle n^2 = \frac{36}{49} \)
\( \displaystyle n = \pm\frac{6}{7} \)
The angle \(\gamma\) with the z-axis is obtuse, so \(n = \cos\gamma\) is negative:
\( \displaystyle n = -\frac{6}{7} \)