SOLUTION: Solve the problem: Find the inner product of the vectors <2,5> and <4, -2>. Then state whether the vectors are perpendicular or not.

The inner product (or "scalar product" or "dot product") of
vectors  and  is the scalar number ac+bd.

<2, 5> · <4, -2> = (2)(4)+(5)(-2) = 8 + (-10) = -2 

<2,5> is the green vector below.  It's tail is at the origin and its
tip is at the point (2,5).



<4,-2> is the red vector below.  It's tail is at the origin and its
tip is at the point (4,-2)



If the inner product of two vectors is 0, then they are perpendicular.

Since the inner product of these two vectors is -2, not 0, they are 
not perpendicular.  The angle between them is about 95°, a little
too wide for 90°

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If the vectors had been

<2, 4> · <4, -2>

then their inner product would have been (2)(4)+(4)(-2) = 8 - 8 = 0

then they would have been perpendicular as we can see:



and the angle between those would have been exactly 90°.

Edwin