Find the magnitude of the vector <1,-4,2>. What is the unit vector?

Answer 1

So a vector is made up of coordinates that reference <x, y, z> so <1,-4,2> is just a vector referring to a line from the <0,0,0> point to <1,-4,2> so the way to find the magnitude of a vector is to use pythagorean theorem on all three axis: x, y and z

Magnitude: √x² + y² +z²) which in this case = √1² + (-4)² +2²) = √21)

Now the unit vector = original vector / magnitude of the vector [You can think of this as scaling the vector down to a magnitude of 1]

So the unit vector = <1,-4,2>/√21) = <1/√21), -4/√21), 2/√21)>

Answer:

Magnitude = √21)

Unit vector = <1/√21), -4/√21), 2/√21)>