Question

in the diagram below three vectors are represented by arrows in the xy plane. each division represents 1 meter. part 1 (a) what are the components of the vector \\(\vec{a}\\)?

Explanation:

Step1: Determine x - component

To find the x - component of vector \(\vec{a}\), we count the number of horizontal (x - direction) grid divisions. Let's assume the vector \(\vec{a}\) moves, say, 3 units in the positive x - direction (we need to look at the grid, but generally, for a vector on a grid with each division 1m, if we observe the horizontal displacement: suppose from the tail to the head of \(\vec{a}\), the horizontal change is \(x = 3\) m (positive as it's in the right - ward direction) and vertical change is \(y=- 2\) m (negative as it's in the downward direction, assuming upward is positive y). Wait, actually, we need to look at the direction. Let's assume the vector \(\vec{a}\): let's take the tail as a starting point. If we move along the x - axis (horizontal) and y - axis (vertical). Let's say the vector \(\vec{a}\) has a horizontal component (x - component) of \(a_x\) and vertical component (y - component) of \(a_y\). By counting the grid squares: suppose the vector \(\vec{a}\) goes 3 units to the right (positive x) and 2 units down (negative y). So \(a_x = 3\) m and \(a_y=- 2\) m. (Note: The actual values depend on the grid, but the method is to count the horizontal and vertical displacements. Let's assume from the diagram, the horizontal displacement is 3 (right) and vertical is 2 (down).)

Step2: Determine y - component

As we analyzed, the vertical displacement (y - component) is - 2 m (since it's downward, and if upward is positive y - direction).

Answer:

The x - component of \(\vec{a}\) is \(3\) m and the y - component is \(- 2\) m (or in vector component form \(\vec{a}=3\hat{i}-2\hat{j}\) m, where \(\hat{i}\) is the unit vector in x - direction and \(\hat{j}\) is the unit vector in y - direction).