Question

Find the unit vector in the direction opposite to v=(-5,1).

Answer 1

First find the vector w that is pointing in the opposite direction of v

Answer 2

Then find the unit vector y such that y is pointing in the same direction as w and |y| = 1

Answer 3

so would w=(5,-1 and |y|= sort(26)

Answer 4

w = (5,-1), good

Answer 5

the length of w is |w| = sqrt(26)

Answer 6

you divide each piece of vector w by its length to get the unit vector y (which points in the same direction as w)

Answer 7

so the opposite direction unit vector for v is 5/sqrt(26)+(-1)/sqrt(26)

Answer 8

You can write it as

\[\Large \vec{y} = \frac{5}{\sqrt{26}}i+\frac{-1}{\sqrt{26}}j\]

or as

\[\Large \vec{y} = \left<\frac{5}{\sqrt{26}}, \frac{-1}{\sqrt{26}}\right>\]

the angle brackets signify we have a vector (and not just a point or ordered pair)

Answer 9

Optionally you can rationalize the denominators, but I've seen many cases where the book doesn't rationalize the denominator

Answer 10

thank you!

Answer 11

you're welcome