Chapter 1: Vectors, Lines and Planes
Section 1.4: Cross Product
Example 1.4.4
Find a unit vector orthogonal to the plane containing the vectors A=5 i−3 j+7 k and B=6 i+2 j−3 k.
Solution
Mathematical Solution
The vector
A×B= |ijk5−3762−3| = 9−14−(−15−42)10−(−18) = −55728
is orthogonal to both A and B. Of course, so is its negation, B×A= −A×B. Unit vectors in each of these two directions are
±A×BA×B = ±1−52+572+282−55728 = ±14058 −55728
Maple Solution - Interactive
Initialize
Tools≻Load Package: Student Multivariate Calculus
Loading Student:-MultivariateCalculus
Enter A as per Table 1.1.1.
Context Panel: Assign to a Name≻A
5,−3,7→assign to a nameA
Enter B as per Table 1.1.1.
Context Panel: Assign to a Name≻B
6,2,−3→assign to a nameB
Obtain and normalize the vectors A×B and B×A
Common Symbols palette: Cross-product operator Context Panel: Evaluate and Display Inline
Context Panel: Student Multivariate Calculus≻Normalize
A×B = →normalize
B×A = →normalize
Maple Solution - Coded
Install the Student MultivariateCalculus package.
withStudent:-MultivariateCalculus:
Define the vectors A and B.
A,B≔5,−3,7,6,2,−3:
Obtain the two possible solutions
Apply the Normalize command to the CrossProduct of A and B.
NormalizeCrossProductA,B
NormalizeCrossProductB,A
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