Determine the direction in respect to the positive X axis of the resultant vector from the sum of the vectors A+B+C if:
A= 2.00i + 4.00j
B= 1.00i - 6.00j
C= -8.00i + 8.00j
A+B+C
= -5i + 6j = <-5,6>
tan (theta) = - 6/5 in quadrant II
so theta = appr 130°
To determine the direction of the resultant vector from the sum of vectors A, B, and C, we need to calculate the sum of the x and y components of the vectors and then find the angle between the resultant vector and the positive x-axis.
Let's start by calculating the sum of the x and y components:
For vector A: A = 2.00i + 4.00j
The x component of A = 2.00
The y component of A = 4.00
For vector B: B = 1.00i - 6.00j
The x component of B = 1.00
The y component of B = -6.00
For vector C: C = -8.00i + 8.00j
The x component of C = -8.00
The y component of C = 8.00
Next, we find the sum of the x and y components:
Sum of x components = 2.00 + 1.00 - 8.00 = -5.00
Sum of y components = 4.00 - 6.00 + 8.00 = 6.00
Now, we can calculate the magnitude and angle of the resultant vector using the sum of the x and y components:
Magnitude of the resultant vector = sqrt((-5.00)^2 + (6.00)^2) = sqrt(61)
To find the angle, we use the arctangent function:
Angle = arctan(6.00 / -5.00)
Angle = -50.2 degrees (approximately)
Therefore, the direction of the resultant vector from the sum of vectors A, B, and C with respect to the positive x-axis is approximately -50.2 degrees.