Expert: Paul Klarreich - 8/23/2009

Question
find the component form of v given its magnitude and the angle it makes with the positive x-axis. Sketch v.

Magnitude ||v||=3         angle = 0degree
Magnitude ||v||=2         angle= v in the direction i + 3j

I don't know what to do with these two problem. what should I do first. Please explain it to me step by step because I'm a slow learner. Thank you for your help!

Answer
Questioner: Justin
Country: United States
Category: Advanced Math
Private: No
Subject: Pre-Cal problems
Question: find the component form of v given its magnitude and the angle it makes with the positive x-axis. Sketch v.

Magnitude ||v||=3         angle = 0degree
Magnitude ||v||=2         angle= v in the direction i + 3j

I don't know what to do with these two problem. what should I do first. Please explain it to me step by step because I'm a slow learner. Thank you for your help!
....................................................
Hi, Justin,

It appears you are studying vectors in the plane. Use the fact that:

<x,y> =  |v|(cos t + sin t),  [t is theta]

therefore
x =  |v| cos t
y =  |v| sin t

Now, for your first example, just apply your knowledge of trigonometry.  
Your t is 0.

[Don't tell me you don't know trig -- you said you were a SLOW learner, not a NON-learner.]
.......................

For your second example, you wrote  i + 3j, or <1,3>

If your vector is in that direction, then its components are proportional to <1,3>.  That vector has mag = sqrt(10).  So the constant of proportionality (remember your geometry?) equal to 2/sqrt(10).  Multiply the <1,3> by that.