Final answer:
To compute the curvature of a curve, use the formula k(t) = ||r'(t) x r''(t)|| / ||r'(t)||^3. Apply this to the given position function r(t) = √7ti + etj + e-tk and find the curvature at point P(0, 1, 1).
Step-by-step explanation:
The curvature of a curve is a measure of how much the curve deviates from being a straight line at a given point. To find the curvature of a curve, we can use the formula: k(t) = ||r'(t) x r''(t)|| / ||r'(t)||^3.
In this case, the position function is given as r(t) = √7ti + etj + e-tk. We need to find the curvature at point P(0, 1, 1), so we can substitute the values into the formula. Differentiating the position function twice, we get r'(t) = √7i + e tj - e-tk and r''(t) = e ti + e tj + e-tk.
Substituting these values into the curvature formula, we have k(t) = ||(√7i + e tj - e-tk) x (e ti + e tj + e-tk)|| / ||√7i + e tj - e-tk||^3. Now we can evaluate this expression at point P(0, 1, 1) to find the curvature at that point.