a + b, 2a + 3b, |a|, and |a − b|.

Question

a = 2i + j,    b = i − 5j

Answer 1

Adding and multiplying vectors, you simply add and multiple components.

a+b = (2+1)i + (1-5)j = 3i - 4j

2a+3b = (2*2+3*1)i + (2*1+3(-5))j = 7i - 13j

Then those lines aren't absolute values; they're the magnitude of the vector. We find this by taking the square root of the sum of squares of the components. I'll first find a-b then find the magnitude.

|a| = √(2²+1²) = √5

a-b = (2-1)i + (1+5)j = i+6j

|a-b| = √(1²+6²) = √37