Consider the surface S: z = 4ex^2 - 4xy, where P (0, 1, 1) is a point on S. An equation of the tangent line to S at P, in the direction of the vector v = (−2, −4) corresponds to: Answers in the picture:

Consider the surface S: z = 4ex^2 - 4xy, where P (0, 1, 1) is a point on S. An equation of the tangent line to S at P, in the direction of the vector v = (−2, −4) corresponds to: Answers in the picture:

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 70EQ

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Question

Consider the surface S: z = 4e^{x^2} - 4xy, where P (0, 1, 1) is a point on S. An equation of the tangent line to S at P, in the direction of the vector v = (−2, −4) corresponds to:

Answers in the picture:

А) (г, у, 2) — (0, 1, 1) + t(-2, —4, 8). t € R
|
В) (г, у, 2) — (0, 1, 1) + t(-2, —4, 6), t € R
С) (л, у, 2) — (0, 1, 1) + t(-2, —4, -6). t€ R
D) (г, у, 2) — (0, 1, 1) + t(-2, —4, -8), t € R

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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