Point

Point
Pointer
Dot Product
Producto Punto
6ᐧT
Sixty
120
360
Point Judith
Poinsettia
Punta Cana

Gen.6:6
 "And it repented the LORD that he had made man on the earth, and it grieved him at his heart."

"This is a point that passes by too easily, so I propose to belabor it."~~~William Dean Howells

"Geoff pointed the way and they set off"~~~Malcolm Lowry

 "He always kept his poise

to the top branches, climbing carefully"~~~Robert Frost

 German shorthaired pointer

 Poinsettia

 Dot Product (Producto Punto)

The dot product of a$\mathbf{a}$ with unit vector u$\mathbf{u}$, denoted a⋅u$\mathbf{a}\cdot \mathbf{u}$, is defined to be the projection of a$\mathbf{a}$ in the direction of u$\mathbf{u}$, or the amount that a$\mathbf{a}$is pointing in the same direction as unit vector u$\mathbf{u}$. Let's assume for a moment that a$\mathbf{a}$ and u$\mathbf{u}$ are pointing in similar directions. Then, you can imagine a⋅u$\mathbf{a}\cdot \mathbf{u}$ as the length of the shadow of a$\mathbf{a}$ onto u$\mathbf{u}$ if their tails were together and the sun was shining from a direction perpendicular to u$\mathbf{u}$. By forming a right triangle with a$\mathbf{a}$ and this shadow, you can use geometry to calculate that

(1)$$\begin{array}{}& \mathbf{a}\cdot \mathbf{u}=\parallel \mathbf{a}\parallel \cos \theta ,\end{array}$$

where $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{u}$.

 Punta Cana, República Dominicana

Point Judith Lighthouse and Coast Guard Station, Rhode Island 

Chess:  "Point" "Pointer" "Dot Product" "Producto Punto" "6ᐧT" "Sixty" "120" "Point Judith" "Poinsettia" "Punta Cana" "360"