Question
Download Solution PDFComprehension
Direction: Consider the following for the items that follow:
Let S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8.
Which of the following are the direction ratios of S?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
⇒ Two planes are x + y + z = 1 and 2x + 3y – 4z = 8.
Let a, b, c are direction ratios of lines of intersection of planes.
Then the lines is perpendicular to normal of both planes
⇒ a + b + c = 0 ...(i)
⇒ 2a + 3b – 4c = 0 ....(ii)
⇒ \(\frac{a}{-4-3} = \frac{b}{2+4} = \frac{c}{3-2} = λ \)
⇒ a = – 7λ, b = 6λ c = λ
Thus, Direction ratios are (–7, 6, 1).
∴ Option (b) is correct
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