If the straight lines x - 1k - y - 22 - z - 33 and x - 23 - y - 3k - z - 13 intersect at a point- then the integer k is equal to

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Distance Formula

If the straig...

Question

If the straight lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{3}$ intersect at a point, then the integer $k$ is equal to

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Solution

The correct option is A $- 5$
Given, two lines intersect at a point. Therefore, the shortest distance between them is zero.
$∴ ∣ ∣ ∣ ∣ \begin{matrix} k & 2 & 3 3 & k & 2 1 & 1 & - 2 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow k (- 2 k - 2) - 2 (- 6 - 2) + 3 (3 - k) = 0$
$\Rightarrow 2 k^{2} + 5 k - 25 = 0$
$\Rightarrow (2 k - 5) (k + 5) = 0$
$\Rightarrow k = \frac{5}{2}, - 5$
Hence, integer value of $k$ is $- 5$ .

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If the straight lines x−1k=y−22=z−33 and x−23=y−3k=z−13 intersect at a point, then the integer k is equal to

The correct option is A −5Given, two lines intersect at a point. Therefore, the shortest distance between them is zero.∴∣∣ ∣∣k233k211−2∣∣ ∣∣=0⇒k(−2k−2)−2(−6−2)+3(3−k)=0⇒2k2+5k−25=0⇒(2k−5)(k+5)=0⇒k=52,−5Hence, integer value of k is −5.

If the straight lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{3}$ intersect at a point, then the integer $k$ is equal to