In the given two lines L1-a1-b1 and L2-a2-b2-if b1-b2 then the lines will be definitely parallel-

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Vector Equation for Straight Line

In the given ...

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$In the given two lines L_{1} = a_{1} + {λb}_{1} and L_{2} = a_{2} + {λb}_{2}, if b_{1} = b_{2} then the lines will be definitely parallel .$

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In the given two lines L_{1} = a_{1} + {λb}_{1} and L_{2} = a_{2} + {λb}_{2}, if b_{1} = b_{2} then the lines will be definitely parallel .

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\vec{r} = \vec{a_{1}} + λ \vec{b_{1}} a n d \vec{r} = 2 \vec{a_{2}} + λ \vec{b_{2}}

\frac{[\vec{a_{1}} \vec{b_{1}} \vec{b_{2}}]}{[\vec{a_{2}} \vec{b_{1}} \vec{b_{2}}]}

\vec{r} = 2 \vec{a_{1}} - 3 \vec{a_{2}} + λ \vec{b_{1}} a n d \vec{r} = \vec{a_{2}} + μ \vec{b_{2}}

[\vec{a_{1}} \vec{b_{1}} \vec{b_{2}}] = k [\vec{a_{2}} \vec{b_{1}} \vec{b_{2}}]

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