Understanding the Units of the Dot Product

AI Thread Summary
The dot product of two vectors results in units that are the product of the individual units of each vector. In this case, if vector A has units of Newtons (N) and vector B has units of centimeters per second (cm/s), then the dot product A·B will have units of N·(cm/s). This confirms that the dot product retains the dimensionality of the vectors involved. Understanding these units is crucial for correctly interpreting the physical meaning of the dot product in various applications. The discussion clarifies that the dot product's units are directly derived from the units of the vectors being multiplied.
dishote2003
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Hi, I got a simple question, "dot product" have units?
I mean, if A=(Ax+Ay+Az)N and B=(Bx+By+Bz)(cm/s) , the units of A.B will be N.(cm/s)
Thanks,
Cali
 
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<br /> \vec{A} \cdot \vec{B} = A_x B_x + A_y B_y + A_z B_z<br />

So clearly, the units of the dot product is the product of the units of A and the units of B.
 
Thanks.
 
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