calculus
posted by colt .
Find two unit vectors that make an angle of 60° with
v =
3, 4
(Enter your answer as a commaseparated list of vectors. Round your answers to four decimal places.)

Let's pick an arbitrary value for the first component, say 1.
then let the vector be (1,b)
(1,b)∙(3,4) = (1,b)(3,4)cos60°
3 + 4b = √(1+b^2)(5)(1/2)
6 + 8b = 5√(1+b^2)
36 + 96b + 64b^2 = 25(1+b^2) after squaring both sides
39b^2 + 96b + 11 = 0
Using the quadratic equation, I got
b = .1205 or b = 2.3411
so one vector is (1,.1205 , the other is (1, 2.3411)
however, when I sketched it, I noticed the second vector would make an angle of 120° , which is the supplement of 60°, so let's us
(1, 2.3411)
also you needed unit vectors:
(1, .1205)} = 1.00723 , so we have (1/1.00723)times vector(1..1205)
so one vector is (.9928,  .1196)
in the same way, find the unit vector for (1,2.3411)
I will check my first vector:
LS = (3,4)∙(.9928, .1196) = 2.5
RS = (.9928, .1196) (3,4)cos60°
= 1(5)(1/2) = 2.5
My first vector works!
Respond to this Question
Similar Questions

GED MATH
You are given an equation of the form y = ax2 + bx + c. y = 4x2 + 2x − 3 (a) Use a graphing utility to graph the equation and to estimate the xintercepts. (Use a zoomin process to obtain the estimates; keep zooming in until … 
precal
Find all solutions of the given equation. (Enter your answers as a commaseparated list. Let k be any integer. Round terms to two decimal places where appropriate.) 2 cos θ − 1 = 0 
calculus
Take an 8.5 by 14inch piece of paper and cut out four equal squares from the corners. Fold up the sides to create an open box. Find the dimensions of the box that has maximum volume. (Enter your answers as a commaseparated list. … 
precalculus
Find all solutions of the given equation. (Enter your answers as a commaseparated list. Let k be any integer. Round terms to two decimal places where appropriate.) tan^2 θ − 3 = 0 
Calculus
We can find some of the solutions of sin x = 0.2 graphically by graphing y = sin x and y = 0.2 (I was able to figure this one out) Use the graph below to estimate some of the solutions. (Let −3π < x < 3π.) Enter … 
Precal
Solve the given equation. (Enter your answers as a commaseparated list. Let k be any integer. Round terms to two decimal places where appropriate.) cos θ = 0.16 I know how to find the answers when it's in fraction form, however, … 
Pre cal
A parallelogram has sides of lengths 7 and 4, and one angle is 55°. Find the lengths of the diagonals. (Round your answers to two decimal places. Enter your answers as a commaseparated list.) 
precalc
Solve the equation. (Enter your answers as a commaseparated list. Round your answers to four decimal places.) 2^x − 8(2^−x) + 2 = 0 
calculus
Solve the given equation. (Enter your answers as a commaseparated list. Let k be any integer. Round terms to two decimal places where appropriate.) tan θ = −square root of 3 
calculus
Solve the given equation. (Enter your answers as a commaseparated list. Let k be any integer. Round terms to two decimal places where appropriate.) tan θ = −square root of 3 answer in radian and please use the k integer