Discussion
If the straight line passing through the points (1,-1,2) and (3,2,8) makes angle \(\beta\) with the y-axis, then the value of \(\cos\beta\) is equal to
Answer: B
\(\cos\beta = \frac{3}{7}\).
The direction ratios of the line are the differences of the coordinates:
\[ \begin{aligned} (3 - 1,\ 2 + 1,\ 8 - 2) &= (2, 3, 6) \\ \sqrt{2^{2} + 3^{2} + 6^{2}} &= \sqrt{49} = 7 \end{aligned} \]
The direction cosines are \(\frac{2}{7}, \frac{3}{7}, \frac{6}{7}\). The angle with the y-axis uses the second one, so \(\cos\beta = \frac{3}{7}\). The option \(\frac{2}{7}\) is the cosine of the angle with the x-axis.
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