Final answer:
The question pertains to the magnitude of the resultant vector when given accelerations at a certain time in a Physics context. The magnitude is calculated using the Pythagorean theorem for three-dimensional vectors, and for vectors of equal magnitude and opposite direction, the resultant is zero.
Step-by-step explanation:
The student is asking about vector addition and vector magnitudes in relation to acceleration (a) and its rate of change over time (a-dot), which are topics in Physics. Specifically, they seem to be looking to determine the magnitude of the resultant vector when two accelerations at a certain instant are known. Considering the example given where a(t) = 5.0i + 2.0j - 6.0k m/s2 and the magnitude is found as |a(2.0 s)| = √(5.02 + 4.02 + (-24.0)2) = 24.8 m/s2, we can understand how to calculate magnitudes. We use the Pythagorean theorem to find the resultant magnitude in three dimensions, which is essentially the length of the diagonal in a rectangular prism formed by the vectors' components.
If two vectors are equal in magnitude and opposite in direction, their resultant vector will have a magnitude of zero since they cancel each other out. This is characteristic of vectors where addition of a vector A and its negative, -A, will lead to a zero resultant.