Thursday

August 25, 2016
Posted by **colt** on Wednesday, August 31, 2011 at 12:46pm.

v =

3, 4

(Enter your answer as a comma-separated list of vectors. Round your answers to four decimal places.)

- calculus -
**Reiny**, Wednesday, August 31, 2011 at 8:24pmLet'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!