If the straight lines x-1-k- y-2-2- z-3-3 x-2-3- y-3-k- z-1-2 intersect at a point- then the value of k equals

The correct option is D 5 The line x x_1/a_1=y y_1/b_1=z z_1/c_1 and #160; x x_2/a_2=y y_2/b_2=z z_2/c_2 #160;intersect if #160; x_ ...

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Byju's Answer

Standard XII

Mathematics

Singular and Non Singualar Matrices

If the straig...

Question

If the straight lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ & $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2}$ intersect at a point, then the value of $k$ equals

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Solution

The correct option is D $- 5$
The line $\frac{x - x_{1}}{a_{1}} = \frac{y - y_{1}}{b_{1}} = \frac{z - z_{1}}{c_{1}}$ and $\frac{x - x_{2}}{a_{2}} = \frac{y - y_{2}}{b_{2}} = \frac{z - z_{2}}{c_{2}}$

intersect if $∣ ∣ ∣ ∣ \begin{matrix} x_{2} - x_{1} & y_{2} - y_{1} & z_{2} - z_{1} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} \end{matrix} ∣ ∣ ∣ ∣ = 0$

$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & - 2 k & 2 & 3 3 & k & 2 \end{matrix} ∣ ∣ ∣ ∣ = 0$

$\Rightarrow 2 k^{2} + 5 k - 25 = 0$

$\Rightarrow (2 k - 5) (k + 5) = 0$

$\Rightarrow$ $k = - 5, k = \frac{5}{2}$ , but $k = \frac{5}{2}$ rejected as $k$ is not an integer.

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If the straight lines x−1k=y−22=z−33 & x−23=y−3k=z−12 intersect at a point, then the value of k equals

If the straight lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ & $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2}$ intersect at a point, then the value of $k$ equals