# Writing a linear combination of unit vectors in cartesian

Then the green polygon is translated along the red vector; the result is the red polygon. For every three that we go in the horizontal direction we're going to go four in the vertical direction. This gives us a reasonable way of defining vector addition.

The movements of the ants are made using vectors.

Would it be reasonable to define the "zero vector" as a vector or not? If is a scalar and If is a 2-D vector, then If is a 3-D vector, then Geometric Definition Scalar multiplication stretches and shrinks the length of the vector by the factor.

Another way of thinking about it, let's say we wanted to figure out a vector that goes in the exact same direction but it has one fifth the magnitude, it only has a magnitude of one. By choosing the base vectors to have the initial points at the origin and their terminal points at 1, 0 and 0, 1 respectively, you get a convenient basis for comparing the coordinates of vectors and the coordinates of points.

Scalar Multiplication Scalar multiplication is an operation which takes a scalar,and a vector,and multiplies them together to create a new vector.

### Unit vector matrix

Translate the blue polygon along your new vector. Scalar Multiplication Scalar multiplication is an operation which takes a scalar, , and a vector, , and multiplies them together to create a new vector,. Additionally the order does not matter because of the parallelogram law. If and are 2-D vectors, then If and are 2-D vectors, then Geometric Definition The vector is added to by placing the tail of at the tip of in a tip to tail diagram. Unit vectors Video transcript What I want to do in this video is explore the idea of a unit vector. If we scale everything down by a fifth, if we were to multiply each of these components of our vector A by a fifth, or another way of thinking about it, if we divide each of these by the magnitude of A then we can construct this unit vector. You can verify.

What's that going to be? That plus that is Find a unit vector in the direction of a given vector. If you succeed with the task, you have created a translation that has the same effect as two translations. Unit vectors Unit vectors are vectors that have the length one unit.

It goes in the same direction but magnitude is one, that's why it's a unit vector.

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