The dot product appears all over physics: Apply the directional growth of one vector to another. Understanding the Dot Product. What's the dot product now?

Understanding the Dot Product Vector Calculus: I prefer "along the path". Need an extra hand? Here's some analogies that click for me:.

Understanding Divergence Vector Calculus: Today we'll build our intuition for how the dot product works. In This Series Vector Calculus: Multiply by a constant: O The expression is meaningless. Take two vectors, a and b. Accumulate the growth contained in several vectors.

The cross product is defined only for two vectors. It shouldn't change just because we tilted our head.

Take a deep breath, and remember the goal is to embrace the analogy besides, physicists lose track of negative signs all the time. It is a vector. Another way to see it: Think of the dot product as directional multiplication.

Imagine the red vector is your speed x and y direction , and the blue vector is the orientation of the boost pad x and y direction. Larger numbers are more power. Photo source.

## Vector Calculus: Understanding the Dot Product

Applying 0,4 to 3,0 means "Destroy your banana growth, quadruple your orange growth". Typical multiplication combines growth rates: Vector Calculus: See how we're "applying" and not simply adding?

With regular addition, we smush the vectors together: