Answer: direction angle of c is pi/4.
Step-by-step explanation: We can find c by adding the corresponding components of a and b:
c = a + b = ⟨–7, 3⟩ + ⟨–2, –12⟩ = ⟨–9, –9⟩
To find the magnitude of c, we can use the formula:
|c| = sqrt(c1^2 + c2^2)
where c1 and c2 are the x- and y-components of c, respectively. In this case, we have:
|c| = sqrt((-9)^2 + (-9)^2) = sqrt(162) = 9sqrt(2)
To find the direction angle of c, we can use the formula:
theta = atan(c2 / c1)
where theta is the angle between the positive x-axis and the vector c. In this case, we have:
theta = atan((-9) / (-9)) = atan(1) = pi/4
So the direction angle of c is pi/4.
Therefore, the magnitude of c is 9sqrt(2) and the direction angle of c is pi/4.