Question

A particle moving in 3-space has position function r(t) = (3√ 2)ti e^(3t) j e^(-3t).

Options:
a) r(t) = (3√ 2)t e^(3t) i + e^(-3t) j
b) r(t) = (3√ 2)e^(3t) ti + e^(-3t) j
c) r(t) = (3√ 2)ti e^(3t) + e^(-3t) j
d) r(t) = (3√ 2)t e^(3t) i - e^(-3t) j

Answer 1

Correct interpretation of a position function in vector notation requires each vector component to be followed by its respective scalar multiplier. The correct notation is option c: r(t) = (3\u221a 2)ti + e^(3t) j + e^(-3t) k.

Step-by-step explanation:

The question involves interpreting a position function given as r(t) = (3\u221a 2)ti e^(3t) j e^(-3t) and choosing the correct notation for it from the given options. In vector notation, each component of the position function is separated by a plus or minus sign, and each unit vector (i, j, k) is associated with its respective scalar function. Hence the correct notation for the position function given should represent the i and j components of the vector function along with their scalar multipliers clearly.

Looking at the options, the correct notation that matches the given function and maintains proper vector representation standards is

• r(t) = (3\u221a 2)ti + e^(3t) j + e^(-3t) k

Therefore, option c is the accurate choice: r(t) = (3\u221a 2)ti + e^(3t) j + e^(-3t) k.