Question

The vector of length 10 and in the same direction as v=<4,−5> is?

The vector in the opposite direction to u=<5,−1> and of half its length is?

Answer 1

The vector of length 10 and in the same direction as v=<4,−5> is?

one way is find the length of v and divide v by this length. It will now have a length of 1
multiply by 10 and you get the vector you want

Answer 2

can you find the length of vector v ?
use sq rt (v dot v)

Answer 3

sqrt41

Answer 4

so divide both components by sqrt(41) and multiply both components by 10

<4,−5>*10/sqrt(41)

you might rewrite 1/sqrt(41) as sqrt(41)/41
so
< 4 , -5 > *10*sqrt(41)/41

Answer 5

The vector in the opposite direction to u=<5,−1> and of half its length is?

multiply both components by -1 to go in the opposite direction
multiply by 1/2 to make it half its size:

so -1/2 * < 5,-1>

Answer 6

thanks