Answer
2.23m
Work Step by Step
In Q 48.a we found that vector a is $26.5^{\circ}$ from the x-axis.
This equation says there are 2 vectors perpendicular to vector a still on the xy plane, vector c and vector d.
The question also says that vector d has a positive x component and vector c has a negative x component.
Which means that vector d is going to be in the 2nd quadrant and vector d is going to be in the 4th quadrant.
To find to the angle between vector c and the x-axis we add the angle between vector a and the x-axis ($26.5^{\circ}$) to the sum of angles from the x-axis of the 1st quadrant to the 3rd quadrant ($90^{\circ} +90^{\circ} +90^{\circ} =270^{\circ}$)
Angle between vector c and x- axis =$270^{\circ}+26.5^{\circ} = 296.5^{\circ}$
We were given the magnitude of vector c as 5m, so we can use this with the angle to find its x-component.
x-component of vector c = $ 5\times cos (295.5^{\circ}) = 2.23m$
