Question 346124
<pre><font size = 4>
The inner product (or "scalar product" or "dot product") of
vectors <a, b> and <c, d> 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).

{{{ drawing(400,400,-7,7,-7,7,
graph(400,400,-7,7,-7,7),

green(line(0,0,2,5), line(1.6,4.6,2,5),line(2.1,4.6,2,5)) )}}}

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

{{{ drawing(400,400,-7,7,-7,7,
graph(400,400,-7,7,-7,7),
red(line(0,0,4,-2), line(3.6,-1.6,4,-2),line(3.6,-2.1,4,-2)),
green(line(0,0,2,5), line(1.6,4.6,2,5),line(2.1,4.6,2,5)) )}}}

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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<font size = 2>
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:

{{{ drawing(400,400,-7,7,-7,7,
graph(400,400,-7,7,-7,7),
red(line(0,0,4,-2), line(3.6,-1.6,4,-2),line(3.6,-2.1,4,-2)),
green(line(0,0,2,4), line(1.6,3.6,2,4),line(2.1,3.6,2,4)) )}}}

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

Edwin</pre>