A=ax+by B=cx+dy
If a = 5 , b = 5, c = 4 and d = 1.
Find the direction of -A (in degrees): relative to +x
To find the direction of -A relative to +x, we need to determine the angle between -A and the positive x-axis.
First, let's find the vector -A by negating the vector A. Negating a vector involves changing the sign of each component:
-A = -ax - by
Using the given values, we have:
-A = -(5x) - (5y)
= -5x - 5y
Now, to find the direction of -A relative to +x, we can calculate the angle between the -A vector and the positive x-axis. We can achieve this by using the arctangent function with the y-component and x-component of -A:
θ = arctan(y-component / x-component)
Here, the x-component is -5 and the y-component is -5, so we have:
θ = arctan((-5) / (-5))
= arctan(1)
Using a calculator or interpreting the value, we find that arctan(1) is equal to 45 degrees.
Therefore, the direction of -A relative to +x is 45 degrees.