Answer: Hope this helps:
(a) The sum of two vectors a and b in unit-vector notation can be calculated using vector addition:
a + b = (4.3 m)î + (3.4 m)ĵ + (-13.0 m)î + (7.6 m)ĵ
= (4.3 m - 13.0 m)î + (3.4 m + 7.6 m)ĵ
= (-8.7 m)î + (11.0 m)ĵ
(b) The magnitude of a vector can be calculated using the Pythagorean theorem:
|a + b| = √((-8.7 m)² + (11.0 m)²) = 12.8 m
(c) The direction of a vector relative to î can be calculated using the tangent of the angle between the vector and the x-axis (î):
tan(θ) = |(11.0 m) / (-8.7 m)| = 1.26
θ = arctan(1.26) = 57.3°
So, the direction of the vector a + b is 57.3° relative to the x-axis (î).