Parallel Lines MCQ Quiz - Objective Question with Answer for Parallel Lines - Download Free PDF
Last updated on Apr 2, 2025
Latest Parallel Lines MCQ Objective Questions
Parallel Lines Question 1:
If the plane 3x + y + 2z + 6 = 0 is parallel to the line \(\frac{3 x-1}{2 b}\) = 3 − y = \(\frac{z-1}{a}\), then the value of 3a + 3b is
Answer (Detailed Solution Below)
Parallel Lines Question 1 Detailed Solution
Calculation:
Given plane 3x + y + 2z + 6 = 0
and line \(\frac{x-\frac{1}{3}}{\frac{2 b}{3}}=\frac{y-3}{-1}=\frac{z-1}{a}\)
Since, plane is parallel to line, then
⇒ \(3\left(\frac{2 b}{3}\right)+(1)(-1)+2(a)=0\)
⇒ 2b - 1 + 2a = 0
⇒ a + b = \(\frac{1}{2}\)
Now, 3a + 3b = \(\frac{3}{2}\)
Hence option 2 is correct
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Parallel Lines Question 2:
If the plane 3x + y + 2z + 6 = 0 is parallel to the line \(\frac{3 x-1}{2 b}\) = 3 − y = \(\frac{z-1}{a}\), then the value of 3a + 3b is
Answer (Detailed Solution Below)
Parallel Lines Question 2 Detailed Solution
Calculation:
Given plane 3x + y + 2z + 6 = 0
and line \(\frac{x-\frac{1}{3}}{\frac{2 b}{3}}=\frac{y-3}{-1}=\frac{z-1}{a}\)
Since, plane is parallel to line, then
⇒ \(3\left(\frac{2 b}{3}\right)+(1)(-1)+2(a)=0\)
⇒ 2b - 1 + 2a = 0
⇒ a + b = \(\frac{1}{2}\)
Now, 3a + 3b = \(\frac{3}{2}\)
Hence option 2 is correct