Answer:
They ARE parallel
Explanation:
Two vectors are parallel if they are scalar multiples of each other. In other words, vectors u and v are parallel if there exists a scalar k such that u=kv.
In your case, the vectors are 6a+8b and 9a+12b.
Let's see if we can find a scalar 6a+8b=k(9a+12b):
6a+8b=k(9a+12b)
Now, equate the corresponding components of both sides:
For the a components: 6a=9ka
For the b components: 8b=12kb
To make these equations hold for all values of a and b, k should satisfy the following conditions:
6=9k (from the a components)
8=12k (from the b components)
Solve for k in each equation:
k = 6/9 = 2/3
k = 8/12 = 2/3
Since both equations give the same value for k, we can conclude that vectors 6a + 8b and 9a + 12b are indeed parallel, as they can be written as scalar multiples of each other with k= 3/2