Answer:
The direction of 5c + 4d is approximately 19.0° clockwise with
the positive part of x-axis
Explanation:
* Lets talk about the direction of a vector
- If the vector is (x , y), then
# Its magnitude is √(x² + y²)
# Its direction is tan^-1 (y/x)
- The direction is the angle between the positive part of x-axis and
the vector
* Lets solve the problem
∵ c = (2.4 , 0.45) and d = (7 , -4)
- To find 5c + 4d , multiply the two coordinates of c by 5 and the two
coordinates of d by 4
# Multiply c by 5
∴ 5c = [5(2.4) , 5(0.45)]
∴ 5c = (12 , 2.25)
# Multiply d by 4
∴ 4d = [4(7) , 4(-4)]
∴ 4d = (28 , -16)
- Lets add 5c and 4d
∴ 5c + 4d = (12 , 2.25) + (28 , -16)
∴ 5c + 4d = [(12 + 28) , (2.25 + -16)]
∴ 5c + 4d = (40 , -13.75)
- The vector is in the 4th quadrant because the x-coordinate is
positive and the y-coordinate is negative
* Find the direction of 5c + 4d
∵ The direction is tan^-1 (y/x)
∴ The direction is tan^-1 (-13.75/40) = -18.97°
* The direction of 5c + 4d is approximately 19.0° clockwise with
the positive part of x-axis