Final answer:
The direction cosines of the line passing through the two points (-2, 3, -4) and (1, 2, 3) are (3/sqrt(59), -1/sqrt(59), 7/sqrt(59)).
Step-by-step explanation:
To determine the direction cosines of the line passing through the two points (-2, 3, -4) and (1, 2, 3), we can find the components of the line. The x-component is given by (1 - (-2)) = 3, the y-component is given by (2 - 3) = -1, and the z-component is given by (3 - (-4)) = 7.
Next, we can find the magnitude of the line using the formula sqrt(x^2 + y^2 + z^2). Substituting the components into the formula, we get sqrt(3^2 + (-1)^2 + 7^2) = sqrt(59).
Finally, we can find the direction cosines by dividing each component by the magnitude. The direction cosines are (3/sqrt(59), -1/sqrt(59), 7/sqrt(59)).