Difference of Scalar Multiples of Vectors:

d = 2a - 3b,

where a = 5i -3j + 2k, and b = -4i + j - 3k.

We handle the scalar constant by simply multiplying each component by it:

2a = 10i - 6j + 4k

3b = -12i + 3j - 9k.

Now we take the difference as usual:

d = (10 - (-12))i + (-6 - 3)j + (4 - (-9))k

= 22i - 9j + 13k.