Finding Unit Vectors and Direction

Pre-Calculus · Axiom Academy

EXAMPLE Finding Unit Vectors and Direction Turn a magnitude and direction angle into component form, then into a unit vector. A vector has magnitude and direction angle . (a) Write in component form . (b) Find the unit vector in the same direction. points into Quadrant III: an angle of lands below and left of the origin, so both components come out negative. Nice work. You converted a magnitude and direction into components, then scaled down to the unit vector — the two everyday moves for working with vectors. Magnitude & direction → components: . Here that gave . Mind the quadrant: the signs of and come from where lands. At (Quadrant III) both are negative. Unit vector = divide by the magnitude: , which always has length 1 . Here . The shortcut: a unit vector in direction is just — so dividing by the magnitude undoes the scaling, and matches exactly. The other direction works the same way: given , the magnitude is and the direction angle is , adjusted for the quadrant.

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