Final answer:
The magnitude of the vector 'a - 3b - 14i - 14j', where vector 'a' has its terminal point at (2,5), and vector 'b' has its initial point at (-1,3) and terminal point at (1,0), is 5.66.
Step-by-step explanation:
To find the magnitude of the vector 'a - 3b - 14i - 14j' we first need to find the vectors 'a' and 'b'.
We can use the coordinates to find the 'a' and 'b' vectors. Here, vector 'a' has its terminal point at (2,5), meaning it's represented as 'a = 2i + 5j'. For vector 'b', with its initial point at (-1,3) and terminal point at (1,0), you determine the difference between the terminal and initial points in each respective dimension, yielding 'b= 2i - 3j'.
Substituting these vectors into the equation 'a - 3b - 14i - 14j' we get '-4i -4j'
The magnitude of a vector V = ai+bj is given by √(a² +b²). Thus, the magnitude of the vector is √((-4)² + (-4)²) = √32 = 5.66.
Learn more about Vector Magnitude