Final answer:
To find the magnitude of a vector, use the formula |v| = √(v_x)² + (v_y)² + (v_z)², where v_x, v_y, and v_z are the components of the vector in the x, y, and z directions respectively. For the vector w = 3.5i + 6.2j - 9k, plugging the values into the formula gives a magnitude of approximately 11.48.
Step-by-step explanation:
To find the magnitude of a vector, we use the formula:
|v| = √(vx)² + (vy)² + (vz)²
where vx, vy, and vz are the components of the vector in the x, y, and z directions respectively.
In this case, the vector w = 3.5i + 6.2j - 9k, so vx = 3.5, vy = 6.2, and vz = -9.
Plugging these values into the formula, we get:
|w| = √(3.5)² + (6.2)² + (-9)²
|w| = √12.25 + 38.44 + 81
|w| = √131.69
|w| ≈ 11.48