Chapter 1: Vectors, Lines and Planes
Section 1.4: Cross Product
Taking A=a1 i+a2 j+a3 k and B=b1 i+b2 j+b3 k, and using Definition 1.4.1, verify that A×B is orthogonal to both A and B.
The orthogonality of each of A and B with A×B is established by showing
Maple Solution - Interactive
Tools≻Load Package: Student Multivariate Calculus
Enter A as per Table 1.1.1.
Context Panel: Assign to a Name≻A
a1,a2,a3→assign to a name
Enter B as per Table 1.1.1.
Context Panel: Assign to a Name≻B
b1,b2,b3→assign to a name
Compute A·A×B and B·A×B
Common Symbols palette: Dot-product and cross-product operators
Context Panel: Evaluate and Display Inline
Context Panel: Simplify≻Simplify
A·A×B = a1⁢a2⁢b3−a3⁢b2+a2⁢−a1⁢b3+a3⁢b1+a3⁢a1⁢b2−a2⁢b1= simplify 0
B·A×B = b1⁢a2⁢b3−a3⁢b2+b2⁢−a1⁢b3+a3⁢b1+b3⁢a1⁢b2−a2⁢b1= simplify 0
Maple Solution - Coded
Install the Student MultivariateCalculus package.
Define the vectors A and B.
Apply the simplify, DotProduct, and CrossProduct commands.
simplifyDotProductA,CrossProductA,B = 0
Of course, replacing A with B in the dot product leads to an equivalent result.
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