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Find a normal unit vector and direction cosines

AA, BB and CC are points (0,1,2)(0,1,2), (3,2,1)(3,2,1) and (1,−1,0)(1,-1,0) respectively.

(i) Find the unit vector perpendicular to both AB→\overrightarrow{AB} and AC→\overrightarrow{AC}.

(ii) Find the cosine of the angles that OB→\overrightarrow{OB} makes with the x-, y- and z-axis.

CJC · Discussion · Question 7

The cross product gives a perpendicular direction; divide by its magnitude to make it a unit vector.

Read the worked solution