Find the magnitude and direction angle of the vector v.

v = 4(cos 125°i + sin 125°j)

||v|| =
θ =

To find the magnitude and direction angle of the vector v, we can use the formula:

Magnitude (||v||) = sqrt((cos(θ) * i)^2 + (sin(θ) * j)^2)

Direction Angle (θ) = arctan(sin(θ) / cos(θ))

Given that v = 4(cos 125°i + sin 125°j), we can substitute the values into the formulas.

Magnitude (||v||) = sqrt((cos(125°) * 4)^2 + (sin(125°) * 4)^2)
Magnitude (||v||) = sqrt((0.5736 * 4)^2 + (0.8192 * 4)^2)
Magnitude (||v||) = sqrt(2.2944^2 + 3.2768^2)
Magnitude (||v||) = sqrt(5.2628 + 10.7307)
Magnitude (||v||) = sqrt(16.9935)
Magnitude (||v||) = 4.1214

To find the direction angle (θ), we can use the fact that cos(θ) = 0.5736 and sin(θ) = 0.8192.

θ = arctan(sin(125°) / cos(125°))
θ = arctan(0.8192 / 0.5736)
θ = arctan(1.427)
θ = 54.083°

Therefore, the magnitude of the vector v is 4.1214 and the direction angle is 54.083°.