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*An Introduction to Classical Mechanic*by K&K. It says:

The solution first begins by recognizing that since the problem is asking to find a unit vector perpendicular toThe problem is to ﬁnd a unit vector lying in the x−y plane that is perpendicular to the vector A = (3, 5, 1).

**A**, then we can conversely say that the dot product of

**A**and

**B**must be equal to zero. And by using the vector component definition of the dot product, [itex]A \cdot B = A_x B_x + A_y B_y = 0[/itex], we can set up our first equation: [itex]3B_x + 5B_y = 0[/itex].

Next, we can say that since it's a unit vector, then the magnitude must be equal to one, and hence [itex]B_x^2 + B_y^2 = 1^2[/itex].

Now we have two equations to solve [itex]B_x[/itex] and [itex]B_y[/itex] with!

I thought this was a great example, neatly combining all the definitions and ideas we'd learned so far.