Final answer:
The length of vector x3, when it represents the result of adding vectors x1 and x2, is typically less than the sum of the lengths of vectors x1 and x2, reflecting the triangle inequality principle in vector addition.
Step-by-step explanation:
Comparing the length of vector x3 to the sum of vector x1 and vector x2's length: In the context of vector addition, according to the triangle inequality, the length of a vector obtained by vector addition is never greater than the sum of the lengths of the individual vectors. Therefore, if vector x3 is the result of adding vectors x1 and x2, option (a) Length of x3 is less than the sum of x1 and x2's length would typically be the correct response. This statement reflects that the direct path (resultant vector) is shorter than the sum of paths taken separately.
A case in which the length of x3 is unrelated to the sum of x1 and x2's lengths would be when vectors x1, x2, and x3 are not related by addition or any vector operation; this is then option (d) Length of x3 is unrelated to the sum of x1 and x2's length.