Understanding Unit Tangent Vectors

The video tutorial explains how to find a unit tangent vector to a level curve at a given point with a positive X component. It begins by introducing the concept of tangent and normal vectors, using gradients to find normal vectors, and calculating partial derivatives for gradient components. The tutorial then evaluates the gradient at a specific point to find a normal vector, determines the tangent vector using the negative reciprocal of the slope, and finally calculates the unit tangent vector, ensuring the X component is positive.

What is the main goal of the problem discussed in the video?

• To solve a system of linear equations.

• To determine the maximum value of a function.

• To calculate the area under a curve.

• To find a unit tangent vector to a level curve at a specific point.

What is the relationship between two perpendicular vectors in terms of their slopes?

• Their slopes are both zero.

• Their slopes are positive reciprocals.

• Their slopes are negative reciprocals.

• Their slopes are equal.

How is the x-component of the gradient vector determined?

• By differentiating the function with respect to y.

• By integrating the function with respect to x.

• By finding the average of x and y.

• By differentiating the function with respect to x.

What is the y-component of the gradient vector at the point (-1, 4)?

• 16

• -36

• 5

• 1

What is the slope of the tangent vector if the normal vector has a slope of 9/4?

• 9/4

• 4/9

• -4/9

• -9/4

What is the x-component of the tangent vector with a slope of 4/9?

• 4

• 36

• 9

• 16

How is the unit tangent vector obtained from the tangent vector?

• By subtracting the tangent vector from its magnitude.

• By multiplying the tangent vector by its magnitude.

• By adding the tangent vector to its magnitude.

• By dividing the tangent vector by its magnitude.

What is the magnitude of the tangent vector 9, 4?

• 97

• 16

• 13

• 81

What should be done if the gradient vector has a positive slope?

• Make the x-component negative and the y-component positive.

• Make the x-component positive and the y-component negative.

• Make both components positive.

• Make both components negative.

What is the y-component of the unit tangent vector at the point (-1, 4)?

• 16/97

• 4/97

• 9/97

• 36/97