First slide

Straight lines in 3D

Question

If the line $\frac{x - 2}{3} = \frac{y + 1}{2} = \frac{z - 1}{- 1}$ and the curve $xy = c^{2}, z = 0$ intersect each other then the value of c is

Moderate

A

$\pm 1$
B

$\pm \frac{1}{3}$
C

$\pm 5$
D

none of these

Solution

We have z = 0 for the point, where the line intersects the curve.
Therefore, $\begin{array}{l} \frac{x - 2}{3} = \frac{y + 1}{2} = \frac{0 - 1}{- 1} \\ \Rightarrow \frac{x - 2}{3} = 1 and \frac{y + 1}{2} = 1 \\ \Rightarrow x = 5 and y = 1 \end{array}$
$Putting these values in x y = c^{2}, we get$
$5 = c^{2} or c = \pm \sqrt{5}$

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