They are given in component vector form. "i" represents the unit vector in the x direction, "j" represents the unit vector in the y direction, and "k" represents the unit vector in the z direction. If one number is given that means the vector is directed in only that direction and has no components in the other directions.BrettL789123 said:how do you graph them? how do you graph one that just gives you 1 number?
A vector is a mathematical object that has both magnitude (size) and direction. It is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction of the vector.
The magnitude of a vector is its size or length. It is a scalar value, meaning it has only a magnitude and no direction. It is represented by the absolute value of the vector's components, which can be calculated using the Pythagorean theorem.
To calculate the magnitude of a vector, you can use the formula |v| = √(x² + y² + z²), where x, y, and z are the components of the vector in 3-dimensional space. In 2-dimensional space, the formula becomes |v| = √(x² + y²). This is derived from the Pythagorean theorem.
Magnitude and direction are two properties of a vector. Magnitude refers to the size or length of the vector, while direction indicates the orientation of the vector in space. They are both important in fully describing a vector.
When adding or subtracting vectors, the magnitude of the resulting vector is affected by the magnitude of the individual vectors being added or subtracted. If the vectors have the same direction, their magnitudes are added or subtracted, but if they have different directions, the resulting magnitude may be smaller or larger depending on the angle between the vectors.