Student/VectorCalculus/Tangent

Student[VectorCalculus][Tangent] - computes the object tangent to a parameterized curve or surface

	Calling Sequence
	Tangent(f, var)

Parameters

f	-	free Vector, position Vector, or Vector-valued procedure; specify the curve or surface
var	-	expression sequence of type algebraic or expression sequence of the form name=algebraic; specify the point at which the tangent object is computed, and optionally the parameters of the curve

Description

•	The Tangent(f, var) command computes the object tangent to the parameterized curve or surface f at the point specified in the other arguments var. Tangent is a generic command that can accept the parameters of both TangentLine and TangentPlane, except scalar expressions.

•	If f is a Vector, the extra arguments must be equations, since the parameter names are required in this case.

•	If f is a Vector-valued procedure, the parameter names can be omitted, but the extra arguments must all be the same type, either algebraic expressions or equations.

•	If f is a Vector, the output will be a position Vector describing the object tangent to f at the point specified by the other parameters var; this position Vector will use parameter variable names specified in var.

•	If f is a Vector-valued procedure, the output will be a procedure, and will use _t, , as its parameter names, where is the number of parameters in f. This output procedure evaluates to a position Vector.

•	The input Vector is a representation of the graph of the object in question. For example, to calculate the tangent plane to the function f := x^2+y^2, the function should be entered as the Vector <x, y, x^2+y^2>, where x and y are the parameters.

Examples

Vector[column]([[a+x], [b+y], [a^2+b^2+2*x*a+2*y*b]])

(1)

Vector[column]([[-(1/2)*theta*2^(1/2)], [(1/2)*2^(1/2)+(1/2)*phi*2^(1/2)], [(1/2)*2^(1/2)-(1/2)*phi*2^(1/2)]])

(2)

(3)

	See Also
	Student[VectorCalculus], Student[VectorCalculus][SetCoordinates], Student[VectorCalculus][TangentLine], Student[VectorCalculus][TangentPlane], Student[VectorCalculus][TangentVector], Student[VectorCalculus][Vector]