Can you explain or provide step-by-step instructions on how to solve as well as the responses to each prompt in the problem. Please do handwritten. I would like to check my own work.

Vector Practice Problem (Vector Algebra) Consider two vectors A and B shown below. Assume that A and B are dimensionless. In this problem avoid using a calculator since it isn't Onecessary; instead use your knowledge of the relative size of the sides of 30 60- 900 and 450 090 triangles determine the sign of each component from the gures, and use your knowledge dot the relative size of simple square roots. Don't convert your answer to decimals unless you want to do a quick \"sanity check.\" (a) Determine the components (143,143.) and (BI, By) for the two vectors. (b) Suppose z is a unit vector in the direction of the positive 2? axis and j is a unit vector in the direction of the positive 3; axis. Write the vectors A and B in terms of the components you found 1n part A and the unit vectors 5. and 3. Be careful and precise with notation. (c) What is the vector sum of fl. and 3? Write your answer in terms of the unit vectors 1? and j. Is the 5!? component of the vector sum 4+5; positive or negative? What about the y component of the vector sum? Do your responses correspond to what you would expect, given some basic properties of the vectors shown in the sketch? (d) What is the vector sum of fl: and