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Vector Basics - Example 2

In mathematics, a vector (from the Latin "mover") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). Vectors play an important role in physics, especially physics and astronomy, because the velocity and the momentum of an object are expressed by vectors.

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Okay, so we have these two vectors and we wanna find a unit vector pointing in the same direction. Or in other words, we want to find the direction vector. So if you recall direction, vector is just the vector divided by the length. So the first thing to do in both cases here is to actually find the length of the factor. So what is the length of the vector? You? Well, this is gonna be the square root of 12 square plus negative size squared. That's 1 44 plus 25. Because it's the square root of 1 69 which is 13. This is kind of a famous Pythagorean triple. Okay? And then the direction of you. So you with this little hat it will take to me in the direction of you is gonna be you back to you, divided by the length you okay. And then this is just gonna be well, I'm just re scaling each of the components. I'm re scaling the vector. You buy one over the length of you. So that's just re scaling the components. So this will be 12 over 13 and then negative. Five over 13, right and then we can do the same thing for this vector V. So we'll start by finding the length of B, which is just the square root of one squared plus one squared plus one squared just the square root of three. And then the direction of means that be happy is gonna be movie divided by length of B. But dividing the vector by the length of the is the same thing is just dividing Egypt. The components of V by the length of be so aren't over squared three one over squared three on over square root is three.

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Lily A.

Johns Hopkins University

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

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Boston College