`bbu = bbi + bbj, bbv = 2bbi - 3bbj` Find (a) `bbu + bbv`, (b) `bbu - bbv`, and (c) `2bbu - 3bbv`.

You need to evaluate the sum of two vectors,`u+v,` hence you need to perform the addition of the same versors, such that:

`u = i + j`

`v = 2i - 3j`

`u + v = (1+2)i + (1-3)j`

`u + v = 3i - 2j`

Hence, evaluating the sum `u + v ` yields `u + v = 3i - 2j`

You need to evaluate the difference of two vectors`,u-v` , hence you need...

You need to evaluate the sum of two vectors,`u+v,` hence you need to perform the addition of the same versors, such that:

`u = i + j`

`v = 2i - 3j`

`u + v = (1+2)i + (1-3)j`

`u + v = 3i - 2j`

Hence, evaluating the sum `u + v ` yields `u + v = 3i - 2j`

You need to evaluate the difference of two vectors`,u-v` , hence you need to perform the subtraction of the same versors, such that:

`u = i + j`

`v = 2i - 3j`

`u - v = (1-2)i + (1+3)j`

`u - v = -i + 4j`

Hence, evaluating the difference `u - v` yields `u - v = -i + 4j.`

You need to evaluate the difference of the vectors,`2u-3v` , hence you need to perform first the multiplication of each vector with the indicated scalar and then you need to perform the subtraction of the same versors, such that:

`u = i + j => 2u = 2i + 2j`

`v = 2i - 3j=> 3v = 6i - 9j`

`2u - 3v =2i + 2j - 6i + 9j => 2u - 3v = -4i + 11j`

Hence, evaluating the difference `2u - 3v` yields `2u - 3v = -4i + 11j.`