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# Let O = (0, 0, 0) as usual. Consider the line consisting of all points Q such that for some real value of t and the line consisting of all

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Let O = (0, 0, 0) as usual. Consider the line consisting of all points Q such that $$\overrightarrow{OQ}= \begin{pmatrix} 7 \\ -3 \\ 1 \end{pmatrix} + \begin{pmatrix} -2 \\ 5 \\ 1 \end{pmatrix} t$$for some real value of t and the line consisting of all points R such that $$\overrightarrow{OR} = \begin{pmatrix} 8 \\ -1 \\ -1 \end{pmatrix} + \begin{pmatrix} 1 \\ -4 \\ 0 \end{pmatrix} u$$ for some real value of u. Enter the point of intersection of the two lines in the usual (a, b, c) format.

Any help would be appreciate, thank you so much!

Mar 2, 2020

#1
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If they intersect at the point (x, y, z) then you have:

7 - 2x = 8 + x

-3 + 5y = -1 - 4y

1 + z = -1

I'm sure you can take it from here.

Mar 2, 2020