What is the magnitude of your displacement when you follow directions that tell you to walk 225 m in one direction, make a 90° turn to the left and walk 350 m, then make a 30° turn to the right and walk 125 m?

The magnitude of the displacement is 291.08 m            

From the given parameters;

Displacement is the shortest distance between the initial position and the final position.

From the image added, the magnitude of the displacement is length PQ.

Apply Pythagoras theorem, t o determine the magnitude of the displacement.

"check the image uploaded"

Thus, the magnitude of the displacement is 291.08 m            

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Start by facing East. Your first displacement is the vector

d₁ = (225 m) i

Turning 90º to the left makes you face North, and walking 350 m in this direction gives the second displacement,

d₂ = (350 m) j

Turning 30º to the right would have you making an angle of 60º North of East, so that walking 125 m gives the third displacement,

d₃ = (125 m) (cos(60º) i + sin(60º) j )

d₃ ≈ (62.5 m) i + (108.25 m) j

The net displacement is

d = d₁ + d₂ + d₃

d ≈ (287.5 m) i + (458.25 m) j

and its magnitude is

|| d || = √[ (287.5 m)² + (458.25 m)² ] ≈ 540.973 m ≈ 541 m

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west