Example 1-4-1 - Maple Help
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Chapter 1: Vectors, Lines and Planes

Section 1.4: Cross Product

Example 1.4.1

For the vectors A=3 i2 j+4 k and B=5 i+7 j6 k, and the scalar c,

a) 

Obtain A×B.

b) 

Obtain θ, the angle between A and B.

c) 

Verify computationally that A×A=0.

d) 

Verify computationally that A×B=A B sin(θ).

e) 

Verify computationally that B×A= A×B.

f) 

Verify that both A and B are perpendicular to A×B.

g) 

Verify that A·B2+A×B2 = A B2.

h) 

Verify that A·B2A×B2 = A B2cos(2 θ).

i) 

Show that A×A×BA×A×B=0.

j) 

Verify that c A×B=cA×B=A×c B.

k) 

Verify that AB×A+B=2A×B.

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