How do I find the dot product of vectors v =5i-2jv=5i−2j and w=3i+4jw=3i+4j?

1 Answer
Gió
Dec 31, 2014

vecv*vecw=7→v⋅→w=7
The dot product is a scalar obtained by multiplying the corresponding components of the two vectors and adding (algebraically) the results.
So you have:
vecv*vecw=(5*3)+(-2*4)=15-8=7→v⋅→w=(5⋅3)+(−2⋅4)=15−8=7

You may check your result by plotting your vectors and using the alternative definition of dot product:

vecv*vecw=|vecv|*|vecw|*cos(theta)→v⋅→w=∣∣→v∣∣⋅∣∣→w∣∣⋅cos(θ)
i.e.: the product of the modulus of the vectors times de cosine of the angle between them.
enter image source here
After some inverse trigonometry and Pitagora's Theorem I got:
|vecv|=5.4∣∣→v∣∣=5.4
|vecw|=5∣∣→w∣∣=5
|theta_v|=21.8°
|theta_w|=53.1°
and theta=21.8°+53.1°=74.9°
so that:
vecv*vecw=5*5.4*cos(74.9°)=7

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