Final answer:
To find the magnitude of the vector v = 6i - 8j, square each component, add them, and take the square root. The magnitude is √(36 + 64), which equals 10.
Step-by-step explanation:
To find the magnitude ||v|| of the vector v = 6i - 8j, we use the Pythagorean theorem for vectors. The magnitude of a vector (also known as its length or norm) for a two-dimensional vector v = ai + bj is given by the square root of the sum of the squares of its components:
||v|| = √(a² + b²)
In this specific case, our vector is v = 6i - 8j. To find its magnitude, we square each component, add them together, and then take the square root:
||v|| = √(6² + (-8)²)
||v|| = √(36 + 64)
||v|| = √100
||v|| = 10
Therefore, the magnitude of the vector v is 10.