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  4. The angle between the lines (x-5/7)=(y+2/-5)=(z/1) and (x/1)=(y/2)=(z/3) is

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Q. 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

Three Dimensional Geometry

Solution:

Direction ratios of the given lines are respectively $7$, $-5$, $1$ and $1$, $2$, $3$.
Now, $a_1 a_2 + b_1 b_2 + c_1c_2 = (7)(1) + (-5)(2) + (1)(3)$
$= 7 - 10 + 3 = 0$
Therefore, the given lines are perpendicular.