Tuesday

September 23, 2014

September 23, 2014

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!

**Answer this Question**

**Related Questions**

calculus - Take an 8.5 by 14-inch piece of paper and cut out four equal squares ...

Calculus - Find the critical numbers of the function. (Enter your answers as a ...

calculus - If x^2 + y^2 = 100 and dy/dt = 6, find dx/dt when y = 8. (Enter your ...

calculus - Determine the value(s) of x where the function will have an ...

calculus - Find any critical numbers of the function. (Enter your answers as a ...

math - given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q ...

math - Take an 17 by 11-inch piece of paper and cut out four equal squares from ...

precalculus - Find all solutions of the given equation. (Enter your answers as a...

precal - Find all solutions of the given equation. (Enter your answers as a ...

calculus - Let f(x) = (x − 3)−2. Find all values of c in (2, 5) such...