Vector Geometry: Determining Parallelism through Dot Products

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Warm up 2 Now, here is a question for you regarding the geometry of dot products, regarding kind ofvisualizing what dot products mean. Suppose I have a vector v over here and then I have vector u over here. And if I extend uas a straight line, I can extend it until it makes a right angle with this vector. This would belike making a right triangle here. Then I have another vector that goes in the same direction as u and up to this point, wherethe right triangle happens. So that other vector is called w, and it's in the same direction asu. Which one is bigger? The dot product of u and v, or the dot product of u and w? Three variants can be there. u dot v can be bigger, u dot w can be bigger, and of coursethey can be equal. Your task is to determine whether the two vectors shown in the picture are parallel basedon the geometry of the diagram and on what you know about dot products.