If the lines r - a 1 - b 1 - and r -2 a 2 - b 2 - are coplanar- then a 1 - b 1 - b 2 - a 2 - b 1 - b 2 -

Given #160;lines #160;are #160;r #8594;=a1 #8594;+ #955;b1 #8594; #160;and #160;r #8594;=2a2 #8594;+ #955;b2 #8594; #160;are #160; ...

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Vector Equation for Straight Line

If the lines ...

Question

If the lines $\vec{r} = \vec{a_{1}} + λ \vec{b_{1}} a n d \vec{r} = 2 \vec{a_{2}} + λ \vec{b_{2}}$ are coplanar, then $\frac{[\vec{a_{1}} \vec{b_{1}} \vec{b_{2}}]}{[\vec{a_{2}} \vec{b_{1}} \vec{b_{2}}]}$ = _____________.

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\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}}

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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

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 .

(a_{1}, b_{1})

(a_{2}, b_{2})

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a_{1} b_{2} = a_{2} b_{1}

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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