Question
Download Solution PDFThe angle between the lines 3x = 3y = -2z and 2x = -y = -3z is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The lines 3x = 3y = -2z and 2x = -y = -3z
Concept:
Use formula for angle between two vectors a and b
\(\rm \cos\theta=\frac{a\cdot b}{|a||b|}\)
Calculation:
The lines 3x = 3y = -2z and 2x = -y = -3z
The the standard form is
\(\rm \frac{x}{1/3}=\frac{y}{1/3}=\frac{z}{-1/2}\) and \(\rm \frac{x}{1/2}=\frac{y}{-1}=\frac{z}{-1/3}\)
Then the direction ratios of given lines are
\(\rm (\frac{1}{3},\frac{1}{3},\frac{-1}{2})\ \ and \ (\frac{1}{2}, -1, \frac{-1}{3})\)
Now let angle between lines is θ then
\(\rm \cosθ=\frac{(\frac{1}{3},\frac{1}{3},\frac{-1}{2})\ \cdot \ (\frac{1}{2}, -1, \frac{-1}{3})}{|(\frac{1}{3},\frac{1}{3},\frac{-1}{2})|\ \cdot \ |(\frac{1}{2}, -1, \frac{-1}{3})|}\)
\(\rm \cosθ=\frac{\frac{1}{6}-\frac{1}{3}+\frac{1}{6}}{\sqrt{\frac{1}{9}+\frac{1}{9}+\frac{1}{4}}\sqrt{\frac{1}{4}+1+\frac{1}{9}}}\)
cos θ = 0
⇒ θ = 90o
Hence the option (1) is correct.
Last updated on May 26, 2025
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