Find the slope of a line perpendicular to the line passing through the given points P(6,-1) and Q(3,-2)

Sonia Rowland
2022-09-30
Answered

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Joel Reese

Answered 2022-10-01
Author has **17** answers

A line passing through (6,−1) and (3,2)

has a slope of

$m=\frac{(-1)-(-2)}{6-3}$

$=\frac{1}{3}$

If a line has slope m

then any line perpendicular to it has slope $(-\frac{1}{m})$

The slope of a line perpendicular to the line passing through the given points P(6,-1) and Q(3,-2) is (−3)

has a slope of

$m=\frac{(-1)-(-2)}{6-3}$

$=\frac{1}{3}$

If a line has slope m

then any line perpendicular to it has slope $(-\frac{1}{m})$

The slope of a line perpendicular to the line passing through the given points P(6,-1) and Q(3,-2) is (−3)

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The following question seems to me interesting. it gives solution space and required the corresponding system of equation. The question is the following:

Consider the vectors in ${R}^{4}$ defined by

${a}_{1}=(-1,0,1,2)$, ${a}_{2}=(3,4,-2,5)$, ${a}_{3}=(1,4,0,9)$

Find a system of homogeneous linear equations for which the space of solutions is exactly subspace of ${R}^{4}$ spanned by the three given vectors.

First i check the linear independence of the given vectors to see form of the generated space. But after determining i only obtained the result that the rank of the coefficient matrix of the corresponding homogeneous system of equations is 2. i obtained this result by rank-nullity theorem. But i can't go further. Please help.

Thanks in advance...

Consider the vectors in ${R}^{4}$ defined by

${a}_{1}=(-1,0,1,2)$, ${a}_{2}=(3,4,-2,5)$, ${a}_{3}=(1,4,0,9)$

Find a system of homogeneous linear equations for which the space of solutions is exactly subspace of ${R}^{4}$ spanned by the three given vectors.

First i check the linear independence of the given vectors to see form of the generated space. But after determining i only obtained the result that the rank of the coefficient matrix of the corresponding homogeneous system of equations is 2. i obtained this result by rank-nullity theorem. But i can't go further. Please help.

Thanks in advance...

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