Final answer:
To write vector b using component notation, express it as B = Bxî + Byˇ, where Bx and By are the horizontal and vertical components calculated using the coordinates of the vector's start and end points or its magnitude and angle with the horizontal axis.
Step-by-step explanation:
To resolve the vector b using component notation, you need to express it in terms of its horizontal and vertical components, typically denoted as Bx and By respectively. This is usually done by using trigonometry if the magnitude and angle of the vector are known. However, if you have the coordinates of the starting point (b) and the end point (e) of the vector, you can calculate Bx and By by subtracting the origin point coordinates from the end point coordinates. The general form for a vector in two dimensions is B = Bxî + Byˇ.
In a case where the vector b is given in a two-dimensional plane and it has an angle θ with the horizontal axis, the horizontal component Bx can be found using the cosine of the angle, Bx = |b| cos(θ), and the vertical component By using the sine of the angle, By = |b| sin(θ), where |b| is the magnitude of the vector b.