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.
If 〈l, m, n〉 are direction cosines of S, then what is the value. of 43 (I2 - m2 - n2)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
We know: Direction ratios are (–7, 6, 1).
⇒Direction ratios of S are l = \(\frac{-7}{\sqrt86}\)
m = \(\frac{6}{\sqrt86 }, n =\frac{1}{\sqrt86}\)
Thus, 43 (l 2 –m2 –n2 ) = 43 \((\frac{49}{86}- \frac{36}{86} - \frac{1}{86})\)
= 43× 12/86 = 6
∴ Option (a) is correct.
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