Answer:

As vector OT is a scalar multiple of (a + 2b), then vector OT is parallel to (a + 2b).
Explanation:
Given vectors:


Find the vector AB using the given vectors:

If AT : TB = 5 : 1 then AT will be 5/6 of AB, and TB will be 1/6 of AB.


Now we have found vector AT, we can calculate vector OT:

If two vectors are parallel, they are scalar multiples of each other.
Therefore, vectors that are parallel to (a + 2b) are in the form k(a + 2b), where k is the scalar multiple.
As vector OT is a scalar multiple of (a + 2b), where k = 5/6, this proves that vector OT is parallel to (a + 2b).