Final answer:
The magnitude of vector B is approximately 5.5 units, and the angle it makes with the positive x-axis is approximately 82.4 degrees.
Step-by-step explanation:
To find the magnitude of vector B and the angle it makes with the positive x-axis, we can use vector subtraction and trigonometric functions.
Given that vector C is the resultant of vectors A and B, we can express vector B as B = C - A. Substituting the given values, we get B = (2.2i + 3.4j) - (1.5i - 2.0j) = 0.7i + 5.4j.
The magnitude of vector B is found using the Pythagorean theorem: |B| = √(0.7² + 5.4²).
Calculating this gives a magnitude of approximately 5.5 units.
To find the angle θ that vector B makes with the positive x-axis,
we use the inverse tangent function (tan⁻¹ or arctan): θ = tan⁻¹(opposite/adjacent) = tan⁻¹(5.4/0.7).
This yields an angle of approximately 82.4°.