Consider the Einthoven’s triangle of frontal ECG for the electrodes RA, LA, and LL. At the peak of the R-wave, the cardiac vector $M$ points vertically downward with $|M| = 5 \text{ mV}$. The voltages on leads I and II are _________ mV and _________ mV, respectively.
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In ECG vector projection problems, always project the cardiac vector magnitude onto the lead axis using $V = M \cos(\theta)$, where $\theta$ is the angle between the vector and the lead direction.
The Einthoven triangle places the three limb electrodes at the vertices of an equilateral triangle.
Lead axes:
- Lead I: RA → LA (horizontal axis)
- Lead II: RA → LL (axis at −60°)
- Lead III: LA → LL (axis at +60°)
Given: The cardiac vector $M$ has magnitude $5$ mV and points straight downward, i.e., at −90°.
To find the lead voltages, project $M$ onto each lead axis. Lead I projection:
Lead I axis = $0^\circ$.
Angle between $M$ (−90°) and Lead I = 90°.
\[
V_I = |M| \cos(90^\circ) = 5 \times 0 = 0 \text{ mV}
\] Lead II projection:
Lead II axis = −60°.
Angle between $M$ (−90°) and Lead II = 30°.
\[
V_{II} = |M| \cos(30^\circ) = 5 \times \frac{\sqrt{3}}{2} = 4.33 \text{ mV}
\]
Thus, the voltages on (I, II) are:
\[
(0 \text{ mV},\; 4.33 \text{ mV})
\]
