Find out whether the following pair of lines are parallel, non-parallel & intersecting, or non-parallel & non-intersecting.
$_{1} =^i +^j + 2^k + λ (3^i - 2^j + 4^k)$
$_{2} = 2^i +^j + 3^k + μ (- 6^i + 4^j - 8^k)$ .

Open in App

Solution

$\begin{matrix} \to r_{1} = \to a_{1} + λ {\to b}_{1} \to r_{2} = \to a_{2} + μ \to b_{2} \to b_{1} = b_{11} ˆ i + b_{12} ˆ j + b_{13} ˆ k = 3 ˆ i - 2 ˆ j + 4 ˆ k \to b_{2} = b_{21} ˆ i + b_{22} ˆ j + b_{23} ˆ k = - 6 ˆ i + 4 ˆ j - 8 ˆ k \frac{b_{11}}{b_{21}} = \frac{b_{12}}{b_{22}} = \frac{b_{13}}{b_{23}} = \frac{- 1}{2} \end{matrix}$

since the direction ratios are equal the given pair of lines are parallel

Suggest Corrections

Similar questions

_{1} =^i +^j + 2^k + λ (3^i - 2^j + 4^k)

_{2} = 2^i +^j + 3^k + μ (- 6^i + 4^j - 8^k)

_{1} =^i -^j + 3^k + λ (^i -^j +^k)

_{2} = 2^i + 4^j + 6^k + μ (2^i +^j + 3^k)

\to r = (^i + 2^j + 3^k) + λ (^i -^j +^k)

\to r = (2^i -^j -^k) + μ (-^i +^j -^k)

_{1} = 2^i + 4^j,_{2} =^i + 4^j - 2^k

_{3} =^i +^j +^k

_{3}

_{1},_{2}

_{1} = (^i + 2^j - 3^k) + s (3^i +^j -^k)

_{2} = (4^i +^j -^k) + t (2^i -^j + 3^k)

Join BYJU'S Learning Program