For the curve given by ,find the unit normal vector.
E) None of these

Question

For the curve given by  ,find the unit normal vector. 
E) None of these

Quizplus · Accepted Answer

To find the unit normal vector, we first need to find the unit tangent vector. Taking the derivative of the given curve, we get:

11eaae29_f46f_7a9b_87fe_b3d932cf2f58_TB2067_11

The magnitude of this vector is:

sqrt((2t)^2 + (2t-1)^2 + 1) = sqrt(8t^2 - 4t + 5)

To find the unit tangent vector, we divide by the magnitude:

(2t, 2t-1, 1) / sqrt(8t^2 - 4t + 5)

To find the unit normal vector, we take the derivative of the unit tangent vector and divide by its magnitude:

(-4, -4, 2) / sqrt(8t^2 - 4t + 5)^3

At t = 0, the unit normal vector is:

(-4, -4, 2) / sqrt(5)^3 = (-4/sqrt(125), -4/sqrt(125), 2/sqrt(125)) = 11eaae29_f46f_a1ae_87fe_cf4258548e7b_TB2067_11

Therefore, the answer is C.

For the Curve Given by ,Find the Unit Normal