To calculate the magnitude of a vector, you can use the Pythagorean theorem, which states that the magnitude is equal to the square root of the sum of the squares of the vector's components. In this diagram, the components of the vector would be the length and width of the river. Once you have the components, you can plug them into the formula to find the magnitude.
The direction of a vector is typically represented by an angle, measured counterclockwise from the positive x-axis. In this diagram, the direction of the vector would be the angle between the river and the swimmer's path. You can use trigonometric functions, such as tangent or sine, to determine this angle.
The resultant vector is the vector that represents the combined effect of multiple vectors. In this diagram, the swimmer's motion can be broken down into two vectors: one along the river's current and one perpendicular to it. To find the resultant vector, you can use the parallelogram rule or the head-to-tail method to add these two vectors together.
The negative sign in front of a vector indicates its direction. In this diagram, a negative sign would mean that the vector is pointing in the opposite direction of the positive x-axis. This could represent the swimmer's motion against the current of the river.
The length of a vector, or its magnitude, represents the strength or intensity of the vector's effect. In this diagram, a longer vector would mean a stronger current or a greater distance the swimmer would have to travel. A shorter vector would indicate a weaker current or a shorter distance to cross.
