anonymous
  • anonymous
which vector is normal to the vector with initial point (2, 5) and the terminal point (10, -1)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
i know how to find if a vector is normal to another vector, but i've never had to solve it this way before. i use the dot product. so what would i multiply my options by? my options are: (8, -6) (3, 4) (2, 3) (0, 6)
anonymous
  • anonymous
it's (8, -6) right?
anonymous
  • anonymous
Two vectors \[\overrightarrow P \text{ and }\overrightarrow Q \] are orthogonal ( in other words, P is normalt to Q) if : \[\overrightarrow P \cdot\overrightarrow Q=0\]

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anonymous
  • anonymous
i know that, but when given the points instead of the actual vector, i got confused. the difference between both x values is 8, and the difference between both y values is -6, which is why I thought that the answer was (8, -6)
anonymous
  • anonymous
Since the initial point of the vector is (2, 5) and the terminal point is (10, -1), then : the coordinates of the vectors are : \[\overrightarrow v=\begin{pmatrix}10-2\\-1-5\end{pmatrix}=\begin{pmatrix}8\\-6\end{pmatrix}\] So (8,-6)) isn't what we are looking for, because we are looking for a vector normal to v
anonymous
  • anonymous
8 times anything except 0 is going to be a nonzero number, right? but 6 x -6 is going to be -36 instead of 0. am i forgetting a step?
anonymous
  • anonymous
no wait. i want the two products sum to be 0. so it's b. because (8 x 3) = 24, and (-6 x 4) = -24. add them together and it's 0. right?
anonymous
  • anonymous
exactly !
anonymous
  • anonymous
awesome. thanks!

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