Final answer:
The exact value of ||v||, which is the magnitude of vector v with initial point (-5,1) and terminal point (1,-2), is calculated using the distance formula. The result is ||v|| = 3√5.
Step-by-step explanation:
To find the exact value of ||v||, which represents the magnitude of the vector v, you need to use the distance formula derived from the Pythagorean theorem. This formula calculates the distance between the initial point (-5,1) and the terminal point (1,-2) of the vector, which can also be considered the vector's magnitude.
The formula is: ||v|| = √((x2 - x1)^2 + (y2 - y1)^2), where (x1,y1) and (x2,y2) are the coordinates of the initial and terminal points, respectively. Substituting the given points into the formula, we get ||v|| = √((1 - (-5))^2 + (-2 - 1)^2) = √(6^2 + (-3)^2) = √(36 + 9) = √45. To express this as an exact value, we can simplify the square root: ||v|| = 3√5.