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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If two lines L_{1} = a_{1} + {λb}_{1} and L_{2} = a_{2} + {λb}_{2} are such that b_{1} is parallel to b_{2} and a_{1} \neq a_{2}, then L_{1} and L_{2} will be

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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}}]}

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Two lines whose direction ratios are a1, b1, c1 and a2, b2, c2 are parallel, if

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