Question

which vector is normal to the vector with initial point (2, 5) and the terminal point (10, -1)?

Answer 1

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)

Answer 2

it's (8, -6) right?

Answer 3

Two vectors
\[\overrightarrow P \text{ and }\overrightarrow Q \]
are orthogonal ( in other words, P is normalt to Q) if :
\[\overrightarrow P \cdot\overrightarrow Q=0\]

Answer 4

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)

Answer 5

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

Answer 6

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?

Answer 7

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?

Answer 8

exactly !

Answer 9

awesome. thanks!