Question
Download Solution PDFComprehension
Direction: Consider the following for the items that follow:
Let L : x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P : x + 2y + 3z + 1 = 0 be a plane.
What are the direction ratios of the line?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
L = x + y + z + 4 = 0 = 2x – y – z + 8 and
P = x + 2y + 3z + 1 = 0 is a plane.
⇒ Let direction ratios of line (a, b, c)
Since line is obtained by the intersection of planes.
⇒ x + y + z + 4 = 0 and 2x – y – z + 8 = 0
So a + b + c = 0....(i)
⇒ 2a – b – c = 0...(ii)
Solve (i) and (ii)
⇒\(\frac{a}{-1+1} = \frac{b}{2+1} = \frac{c}{-1-2} =λ \)
⇒ a = 0, b = 3λ and c = –3λ
⇒ Direction ratios of line is (0, 3, –3) or (0, 1, –1).
∴ Option (c) is correct.
Last updated on May 30, 2025
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