Discussion
The angle between the lines \(\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}\) and \(\frac{x}{1}=\frac{y}{2}=\frac{z}{3}\) is
Answer: B
The angle is \(\pi/2\).
The direction ratios are (7, -5, 1) and (1, 2, 3). The cosine of the angle is proportional to their dot product:
\[ 7(1) + (-5)(2) + 1(3) = 7 - 10 + 3 = 0 \]
A zero dot product means the lines are perpendicular, so the angle is π/2. An angle of 0 would need proportional direction ratios, and π/3 or π/4 would need a non-zero dot product.
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