What value(s) of "a" will make the vector A = 2i + j + a k have a magnitude equal to 3?

Explanation

The magnitude of vector A is given by √(2² + 1² + a²) = √(4 + 1 + a²) = √(5 + a²). Setting this equal to 3, we get √(5 + a²) = 3, which implies 5 + a² = 9. Solving for a² gives a² = 4, so a = ±2. Therefore, the values of a can be either -2 or 2.