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Question Number 6321 by sanusihammed last updated on 23/Jun/16

Determine ∈ and N by using vector such that point (−1,3,2),  (−4,−2,−2) and (5,∈,N) lies on a straight line

$${Determine}\:\in\:{and}\:{N}\:{by}\:{using}\:{vector}\:{such}\:{that}\:{point}\:\left(−\mathrm{1},\mathrm{3},\mathrm{2}\right), \\ $$$$\left(−\mathrm{4},−\mathrm{2},−\mathrm{2}\right)\:{and}\:\left(\mathrm{5},\in,{N}\right)\:{lies}\:{on}\:{a}\:{straight}\:{line} \\ $$$$ \\ $$

Answered by nburiburu last updated on 23/Jun/16

let′s find the line:  (x;y;z)=(−1;3;2)+λ.[(−4;−2;−2)−(−1;3;2)]  now let be (x;y;z)=(5;ε;N) and you can solve it.  the result should be λ=−2; ε=13; N=10.

$${let}'{s}\:{find}\:{the}\:{line}: \\ $$$$\left({x};{y};{z}\right)=\left(−\mathrm{1};\mathrm{3};\mathrm{2}\right)+\lambda.\left[\left(−\mathrm{4};−\mathrm{2};−\mathrm{2}\right)−\left(−\mathrm{1};\mathrm{3};\mathrm{2}\right)\right] \\ $$$${now}\:{let}\:{be}\:\left({x};{y};{z}\right)=\left(\mathrm{5};\epsilon;{N}\right)\:{and}\:{you}\:{can}\:{solve}\:{it}. \\ $$$${the}\:{result}\:{should}\:{be}\:\lambda=−\mathrm{2};\:\epsilon=\mathrm{13};\:{N}=\mathrm{10}. \\ $$$$ \\ $$

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