Final answer:
The exact value of the vector v with initial point at (-8,5) and a terminal point at (-3,-1) is the square root of 61 or √61, determined by calculating the magnitude (length) of the vector using the Euclidean distance formula.
Step-by-step explanation:
The exact value of a vector (||v||) can be calculated by determining the magnitude (length) of the vector, using the formula for the Euclidean distance (or the distance formula), given that the vector v has an initial point at (-8,5) and a terminal point at (-3,-1).
The formula for deriving the length/magnitude of a vector is: ||v|| = √[(x2 - x1)² + (y2 - y1)²]. Here, x1, y1 is the initial point, and x2, y2 is the terminal point.
Therefore, applying these points to the formula, we have:
||v|| = √[(-3 - (-8))² + (-1 - 5)²] = √[(5)² + (-6)²] = √[25 + 36] = √61.
So, ||v||, the exact value of vector v, is √61.
Learn more about Vector Magnitude