Question

Find two unit vectors that make an angle of 60° with v = ‹6, 8›. Give your answers correct to three decimal places.

Answer 1

v*x = |v||x| cos 60

Answer 2

x/|x| = (|v| cos 60 )/v

Answer 3

i know \[\left| v \right|\] = 10 but im not for sure on the rest

Answer 4

|v|cos 60 = 5
5/v = <5/6, 5/8 > but |<5/6, 5/8 >| does not quite equal 1 so Im tripping

Answer 5

no it doesnt...1.04

Answer 6

converting v to unit vector...

Answer 7

Let u = ha, bi be a unit vector. By Theorem 3 we need u·v = |u| |v| cos 60◦
⇔ 4a + 3b = (1)(5) 1
2 ⇔
b = 5
2·3 − 4
3a. Since u is a unit vector, |u| = √a2 + b2 = 1 ⇔ a2 +b2 = 1
⇔ a2 + 􀀀5
6 − 4
3a2
= 1 ⇔ ⇔ 100a2 − 80a − 11 = 0.
By the quadratic formula, a = −(−80) ±p(−80)2 − 4(100)(−11)
2(100)
=
80 ± √10800
200
.
If a =
20 + √2700
25 ≈ 0.92 then b =
5
6 −
4
3
(0.919615)
≈ −0.393 , and if a =
20 − √2700
25 ≈ −0.12 then b =
5
6 −
4
3
(−0.119615)
≈ 0.993 . Thus the two unit vectors are h0.92,−0.393i and h−0.12, 0.993i.

Answer 8

this was with <4,3>

Answer 9

I crashed :(

let me check my latest

Answer 10

lol...ok

Answer 11

<5/6, 5/8> is sooo close, Im thinking precision error :)

Answer 12

1.0416666...

Answer 13

so then what is the other vector?

Answer 14

so v hat is <3/5,4/5>
then v*x = |v||x| cos 60 becomes v*x = cos 60

Answer 15

for the other vector flip the y axis, cos 60 = cos -60