Finding the Tangent Vector at a Point

Thread starter soccer43
Start date Sep 22, 2011
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Point Tangent Tangent vector Vector

In summary, a tangent vector at a point is a vector that represents the direction and rate of change of a curve at that specific point. It is calculated by taking the derivative of the curve at that point and has significance in understanding the behavior of the curve and calculating the direction and rate of change of an object moving along the curve. The relationship between the tangent vector and the normal vector at a point is that they are perpendicular to each other, with the tangent vector representing the direction of the curve and the normal vector representing the direction perpendicular to the curve. The tangent vector at a point can also be negative, indicating a decrease in the curve or an object moving in the opposite direction of the tangent vector.

Sep 22, 2011

soccer43

I can use the tangent vector and a point.

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Sep 23, 2011

lanedance

Homework Helper

can you explain your method, or what the question actually asks?

What is a tangent vector at a point?

A tangent vector at a point is a vector that is tangent to a curve at a specific point. It represents the direction and rate of change of the curve at that point.

How is the tangent vector at a point calculated?

The tangent vector at a point can be calculated by taking the derivative of the curve at that point. This will give the slope of the curve, which is the direction of the tangent vector, and the magnitude of the derivative will give the rate of change.

What is the significance of finding the tangent vector at a point?

Finding the tangent vector at a point is important in understanding the behavior of a curve at that point. It can also be used to calculate the direction and rate of change of a particle or object moving along the curve at that point.

What is the relationship between the tangent vector and the normal vector at a point?

The tangent vector and the normal vector at a point are perpendicular to each other. The tangent vector represents the direction of the curve, while the normal vector represents the direction perpendicular to the curve.

Can the tangent vector at a point be negative?

Yes, the tangent vector at a point can be negative. This indicates that the curve is decreasing at that point, or that the object moving along the curve is moving in the opposite direction of the tangent vector.