Show that the lines x-5/7=y+2/-5=z/1 and ...

NCERT Class XII Mathematics Chapter - - Solutions

Question : 20 of 78

Marks: +1, -0

Show that the lines

\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}

and

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}

are perpendicular to each other.

Solution:

Direction ratios of the given lines are < 7, –5, 1> and < 1, 2, 3> respectively. Since 7 × 1 + (– 5) × 2 + 1 × 3 = 0. Therefore the given lines are perpendicular.

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