Understanding the Units of the Dot Product

Thread starter dishote2003
Start date Feb 19, 2004
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Dot Dot product Product Units

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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.

Feb 19, 2004

dishote2003

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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Feb 19, 2004

Tron3k

<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.

Feb 24, 2004

dishote2003

Thanks.

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