Find equation of tangent plane to surface at given point

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Find an equation of the tangent plane to the given parametric surface at the specified point.

r(u, v) = u cos vi + u sin vj + vk; u = 5, v = π/3

Equation of tangent plane to given parametric equation is:

Step-by-step explanation:

Given equation

---(1)

Normal vector  tangent to plane is:

Normal vector  tangent to plane is given by:

Expanding with first row

at u=5, v =π/3

---(2)

at u=5, v =π/3 (1) becomes,

From above eq coordinates of r₀ can be found as:

From (2) coordinates of normal vector can be found as

Equation of tangent line can be found as:

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