Question

Find the magnitude of \(v\). Initial point of \(\mathbf{v}:(0,-1,0)\) Terminal point of \(\mathbf{v}:(1,2,-2)\)

Short answer

The magnitude of the vector \(v\) is \(3.74\).

Step-by-step solution

Calculate the components of the vector

Calculate each component as the difference between the coordinates of the terminal point and the initial point. The x component \(v_x\) is given by: \(v_x = x_{terminal} - x_{initial}\). Similarly, calculate \(v_y\) and \(v_z\). In our case, \(v_x = 1 - 0 = 1\), \(v_y = 2 - (-1) = 3\) and \(v_z = -2 - 0 = -2\).

Calculate the square of each component

Each component is squared: \({v_x}^2 = 1^2 = 1\), \({v_y}^2 = 3^2 = 9\) and \({v_z}^2 = -2^2 = 4\).

Calculate the sum of the squares

The sum of the squares is: \(1 + 9 + 4 = 14\).

Find the square root of the sum

The square root of the sum is the magnitude of the vector: \(|v| = \sqrt{14} = 3.74\) (rounded to two decimal places).