paralle M =< 5t, 1 – t,3+4t > be on planes Q and R respectively. A clear writing is expected.) (a) Why are the lines L and M not parallel? Explain

Linear Algebra: A Modern Introduction
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Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
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please solve part (b), ( c) and (d)
Consider two parallel planes Q and R. Let the lines L =< 1 – 2t,4 + t,3 > and
M =< 5t, 1 – t,3+4t > be on planes Q and R respectively.
(A clear writing is expected.)
(a) Why are the lines L and M not parallel? Explain.
(b) Why are the planes Q and R not the same plane, without answering part (d) first, or
showing the distance between them is not zero? Explain your reasoning.
(c) Show with reasoning, how you find the equation of the plane Q.
(d) Find the distance between the two parallel planes. Explain your work.
Transcribed Image Text:Consider two parallel planes Q and R. Let the lines L =< 1 – 2t,4 + t,3 > and M =< 5t, 1 – t,3+4t > be on planes Q and R respectively. (A clear writing is expected.) (a) Why are the lines L and M not parallel? Explain. (b) Why are the planes Q and R not the same plane, without answering part (d) first, or showing the distance between them is not zero? Explain your reasoning. (c) Show with reasoning, how you find the equation of the plane Q. (d) Find the distance between the two parallel planes. Explain your work.
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