Show that the lines 7 = - 5 = 1 and 1 = 2 = 3 are perpendicular to each other.

. : Direction ratios of the given lines are respectively and . Since 7 1 + ( - 5) 2 + 1 3 = 0 therefore , the given lines are perpendicular.

Three Dimensional Geometry — Class 12 Maths Solution

ncert exercise SA NCERT,EX.11.2,Q.13, Page .478

Question

Show that the lines $\cfrac{{x - 5}}{7} = \cfrac{{y + 2}}{{ - 5}} = \cfrac{z}{1}$ and $\cfrac{x}{1} = \cfrac{y}{2} = \cfrac{z}{3}$ are perpendicular to each other.

Step-by-step Solution

. : Direction ratios of the given lines are respectively

$< 7, - 5,1 >$ and $< 1,2,3 >$.

Since $7 \times 1 + ( - 5) \times 2 + 1 \times 3 = 0$

therefore , the given lines are perpendicular.

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Three Dimensional Geometry. Curated by Sachin Sharma. Free for all students.