(A) Vectors in Cartesian Coordinates
1. A unit vector is a vector whose magnitude is one unit.
2. A unit vector that is parallel to the x-axis is denoted by while a unit vector that is parallel to the y-axis is denoted by .
3. The unit vector can be expressed in columnar form as below:
4. The magnitudes of the unit vectors are
5. The magnitude of the vector can be calculated using the Pythagoras’ Theorem.
(B) Unit Vector in the Direction of a Vector
If and , find the values of k. Determine the unit vector in the direction of for each value of k.
It is given that
(b) Hence, find the unit vector in the direction of