Chapter 1: Vectors, Lines and Planes
Section 1.3: Dot Product
Example 1.3.15
If A=ax i+bx j and B=ux i+vx j, verify the product rule for differentiating the dot product A·B.
Solution
Mathematical Solution
A·B′
=axux+bxvx′
=axux′+bxvx′
=a u′+u a′+b v′+v b′
=a u′+b v′+u a′+v b′
=A·B′+B·A′
Maple Solution - Interactive
In the Student MultivariateCalculus package, differentiation automatically maps onto the components of a vector, just as in the VectorCalculus packages.
Tools≻Load Package: Student Multivariate Calculus
Loading Student:-MultivariateCalculus
Define the vectors A and B
Write A=… as per Table 1.1.1.
Context Panel: Assign to a Name≻A
ax,bx→assign to a nameA
Write B=… as per Table 1.1.1.
Context Panel: Assign to a Name≻B
ux,vx→assign to a nameB
Show the difference between A·B′ and A·B′+B·A′ is zero
Context Panel: Evaluate and Display Inline
A·B′−A·B′+B·A′ = 0
Alternate notation and calculation
Calculus palette: Differentiation operator Common Symbols palette: Dot-product operator
ⅆⅆ x A·B−A·ⅆⅆ x B+B·ⅆⅆ x A = 0
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