JEE Mains · Maths · STD 12 - 11. three dimension geometry
The lines \(x=a y-1=z-2\) and \(x=3 y-2=b z-2,(a b \neq 0)\) are coplanar, if:
- A \(b=1, a \in R-\{0\}\)
- B \(a=2, b=3\)
- C \(a=2, b=2\)
- D \(a=1, b \in R-\{0\}\)
Answer & Solution
Correct Answer
(A) \(b=1, a \in R-\{0\}\)
Step-by-step Solution
Detailed explanation
\(\frac{x+1}{a}=y=\frac{z-1}{a}\) \(\frac{x+2}{3}=y=\frac{z}{3 / b}\) lines are Co-planar \(\left|\begin{array}{ccc}a & 1 & a \\ 3 & 1 & \frac{3}{b} \\ -1 & 0 & -1\end{array}\right|=0 \Rightarrow-\left(\frac{3}{b}-a\right)-1(a-3)=0\) \(a-\frac{3}{b}-a+3=0\) \(b=1, a \in R-\{0\}\)
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