Problem

$$\begin{array}{l}{\text { Suppose a vector a mak…

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Problem 39 Easy Difficulty

Vectorcardiography As the heart beats it generates differences in electrical potential (that is,voltage) across the body. Cardiologists view the voltage at any point in time during a heartbeat as a vector. During ventricular contraction in healthy individuals this vector points downward and to the left of the patient (see the figure). Abnormalities in either the magnitude or direction can be used to diagnose cardiac problems. We can think of the voltage vector as being the resultant
vector of a vertical and a horizontal component of voltage see the figure). Conductive abnormalities in different parts of the heart can reduce the voltage in either of these directions, thereby altering the direction and magnitude of the resultant voltage vector.
$$\begin{array}{l}{\text { (a) A left anterior hemiblock reverses the direction of the }} \\ {\text { vertical component of voltage and reduces the magni- }} \\ {\text { tude of the horizontal component. Describe how such }} \\ {\text { a condition could be diagnosed based on the resultant }} \\ {\text { voltage vector. }}\end{array}$$
$$\begin{array}{l}{\text { (b) A left posterior hemiblock reverses the direction of the }} \\ {\text { horizontal component of voltage. Describe how such }} \\ {\text { a condition could be diagnosed based on the resultant }} \\ {\text { voltage vector. }}\end{array}$$

Answer

a) left anterior hemiblock is diagnosed.
b) left posterior hemiblock is diagnosed.

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Calculus 3

Biocalculus Calculus for the Life Sciences

Chapter 8

Vectors and Matrix Models

Section 2

Vectors

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Video Transcript

All right, so we have the main chute of eye. One is the squared of one. The magnitude of I two is equal to the square root of 1/2 which is one over four plus three over 41 in magnitude by three is also equal to one. So I won dot I two is equal to 1/2 That's here. 1/2 comma zero I want that I three is equal to negative 1/2 court zero. And finally I, too that I three is equal to negative 1/4 comma three Force negative 1/4 comma positive 3/4

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