anonymous 4 years ago Find two unit vectors that make an angle of 60° with v = ‹6, 8›. Give your answers correct to three decimal places.

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

no it doesnt...1.04

6. anonymous

converting v to unit vector...

7. anonymous

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.

8. anonymous

this was with <4,3>

9. anonymous

I crashed :( let me check my latest

10. anonymous

lol...ok

11. anonymous

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

12. anonymous

1.0416666...

13. anonymous

so then what is the other vector?

14. anonymous

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

15. anonymous

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