Answer:
magnitud = 10.9 km θ = 15º. the displacements are equal
Explanation:
The sum of vectors can be done by two methods: one graphic and one analytical
In the graphic method, the first vector is drawn, then the second vector is drawn on the end of it and so on, the vector is finely drawn resulting from the origin of the first to the tip of the last. Look at the attachments for our case
When you examine the drawings, you conclude that the displacements are equal, this is because of the commutative property of the addition
a) magnitud = 13.8 km θ = 24º
b) magnitud =13.8 km θ = 24º
analytical method
To find the values, we decompose the vectors, using trigonometry
Ax = 9 cos 60 = 4.5 km
Ay = 9 sin 60 = 7.8 km
Bx = 6 km
Cx = 3 cos 315 = 2.12 km
Cy = 3 sin 315 = -2.12 km
We calculate the result on each axis
Rx = Ax + Bx + Cx
Ry = Ay + By + Cy
Rx = 4.5 + 6 + 2.12
Rx = 12.62 km
Ry = 7.8 +0 -2.12
Ry = 5.68 km
Using Pythagoras and trigonometry we build the resulting vector
R = √(12.62² +5.68²)
R = 13.84 km
tan θ = Ry / Rx
θ = tan⁻¹ (5.68 / 12.62)
T = 24º
