 Hello, and welcome to this screencast on section 9.2, Vectors. This screencast is going to cover geometric interpretation of vector operations. In this screencast, we will visualize some vector operations. Let's start with vector addition and subtraction. On the left graph, if we think of vectors as displacements in the plane, the vector u plus v will represent the displacement of u, followed by the displacement of v. Remember that the position of a vector doesn't matter, so we may picture this by placing the tail of v at the tip of u, as we have in this picture. We can then visualize the vector u plus v in standard position. Vector subtraction can be interpreted similarly. To visualize this, we place both u and v in standard position. Then the vector u minus v is the difference of the displacements from the tip of v to the tip of u. Next, we will visualize scalar multiplication of a vector. Scalar multiplication just means multiplying a vector by a real number, also called a scalar. As the name suggests, this will scale the vector. Pictured here, we have the vector v. The scalar multiple 2 times v would stretch the vector v by a factor of 2 without changing the direction. On the other hand, the scalar multiple negative 2 times v would stretch the vector v by a factor of 2 and point in the opposite direction. Here we see that multiplying by a negative scalar changes the direction of a vector.