Question

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

Answer 1

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)