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Question: Answered & Verified by Expert
If the straight lines $\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$ intersect at a point, then the integer $k$ is equal to
MathematicsThree Dimensional GeometryJEE MainJEE Main 2008
Options:
  • A
    $-5$
  • B
    5
  • C
    2
  • D
    $-2$
Solution:
2445 Upvotes Verified Answer
The correct answer is:
$-5$
$\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$
Since lines intersect in a point
$$
\begin{aligned}
& \left|\begin{array}{ccc}
k & 2 & 3 \\
3 & k & 2 \\
1 & 1 & -2
\end{array}\right|=0 \\
& \therefore 2 k^2+5 k-25=0 \\
& k=-5,5 / 2 .
\end{aligned}
$$
Directions: Questions number 17 to 21 are Assertion-Reason type questions. Each of these questions contains two statements : Statement - 1 (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

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