Final answer:
To find the magnitude of the vector 8 times the vector v = 9i + 3j, we calculate ||8v|| = √(72² + 24²), which simplifies to ||8v|| = 76.
Step-by-step explanation:
To find the magnitude of the vector 8v, which is 8 times the vector v = 9i + 3j, we first multiply the vector by 8 to get 8v = 72i + 24j. Then, to find the magnitude (also denoted as the norm) of this new vector, we use the formula: ||8v|| = √(72² + 24²). Calculating this, we find:
||8v|| = √(5184 + 576) = √5760
Thus, ||8v|| = √5760, which simplifies to ||8v|| = 76 when we take the square root.
The final answer is 76.