00:01
Okay, let's say we have a vector that has a magnitude or length of two, and it goes in the same direction as i plus 3j, which is really the vector 1, because the number in front of i is 1, and the number of front of j is 3.
00:29
So in order to do this to find the component form of a vector with a magnitude of 2 and going in the direction as i plus 3j, we need to basically find the unit vector and then we're going to multiply it by the magnitude.
00:58
Let's do that.
00:59
So if we have i plus 3j, we're going to find its unit vector and then i'm just going to multiply it by the magnitude of 2.
01:07
To get to the vector that i want.
01:10
So how do you find a unit vector? you got to divide by the magnitude of that vector.
01:15
So we have 1 .3.
01:17
So to find its magnitude, we're going to do the square root of 1 squared plus 3 squared.
01:24
1 squared is 1.
01:26
3 squared is 9.
01:28
So we're looking at the square root of 10, which is 2 times 5, so eh, not really simplifiable.
01:34
So to get the unit vector for this, we are going to divide each one of these by the square root of 10.
01:46
And you should probably rationalize your denominator, which would result in us multiplying the top and the bottom by root 10.
02:01
So we end up with the square root of 10 over 10 and 3 root 10 over 10.
02:10
So that is the unit vector.
02:13
But now in order to get the component form of the specific vector we want, we need to multiply that by the magnitude of 2.
02:23
So i'm going to do two times this unit vector.
02:34
So if we do that, we're going to have, you can put this over 1 if it helps, 2 root 10 over 10, and 6 root 10 over 10.
02:47
And now we have some fractions that are simplifiable, so we can simplify the whole numbers that are not under the radical...