Question
Download Solution PDFWhat are the direction ratios of the line of intersection of the planes x = 3z + 4 and y = 2z - 3?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The equation of a line with direction ratio (a, b, c) that passes through the point (x1, y1, z1) is given by the formula: \(\rm \frac{{x - {x_1}}}{a} = \frac{{y - {y_1}}}{b} = \frac{{z - {z_1}}}{c}\)
If two planes intersect each other, the intersection will always be a line.
Calculation:
Given:
x = 3z + 4 and y = 2z - 3
⇒ x - 4 = 3z and y + 3 = 2z
\(\rm \Rightarrow \frac{x - 4}{3} = z \;\text{and} \ \frac{y + 3}{2} = z\)
\(\rm \Rightarrow \frac{x - 4}{3} = \frac{y + 3}{2} = \frac{z}{1}\)
If two planes intersect each other, the intersection will always be a line.
Now, direction ratios of the line are 〈3, 2, 1〉
Last updated on May 31, 2025
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