Find a + b, 2a + 3b, |a|, and |a - b|. a = 5i + j, b = i - 3j

A+b = (5i + j) + (i - 3j) = 6i - 2j

2a + 3b = 2 (5i + j) + 3 (i - 3j) = 10i + 2j + 3i - 9j = 13i - 7j

|a| = sqrt ((5^2) + (1^2)) = sqrt (26)

|a-b| = | (5i+j) - (i-3j) | = |4i+4j| = sqrt ((4^2) + (4^2)) = sqrt (32)