Final answer:
The magnitude of the vector u = ⟨3,4,5⟩ is approximately 7.07 and its direction can be represented as (θ, φ) in spherical coordinates.
Step-by-step explanation:
The magnitude of a vector can be found using the Pythagorean theorem. In this case, the vector u = ⟨3,4,5⟩ has three components, so we can use the formula: magnitude = sqrt(x^2 + y^2 + z^2), where x, y, and z are the components of the vector.
For the given vector, the magnitude = sqrt(3^2 + 4^2 + 5^2) = sqrt(9 + 16 + 25) = sqrt(50) ≈ 7.07
To find the direction of the vector, we can use trigonometry. We can calculate the angles between the vector and each of the coordinate axes using the inverse trigonometric functions. In this case, the direction of the vector can be written as an angle in spherical coordinates, (θ, φ), where θ represents the angle made with the positive x-axis, and φ represents the angle made with the positive z-axis.