Hello, Stuck Man!

The line through the point with direction

can be written in two forms:

. . Symmetric form: .

. . Cartesian form: .

The symmetric form is derived from the Cartesian form.A vector equation of a line in symmetric form is either written

with = t at the right end usually or omitted.

Is this a matter of preference?

. .

Equate [1], [2], [3]: .

The is usually omitted.

Also are the terms symmetric form and Cartesian form referring to the same thing?

Is Cartesian form the more professional term?

Both forms refer to the same line.

The Cartesian form is more convenient for algebraic work.

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An amusing note . . . well,think it's funny.I

Given the point and direction

. . the symmetric equation is: .

This may be the only instance where "division by zero" is defined.