1. Resolving Vectors into Components – the “Vector Collector”
Before adding the vectors,
you should sketch the vectors.
R = J + K
J = 160.km [E25oN]
K = 95.0km [SE] X Y
Jx =
Jy =
Kx =
Ky =
Rx =
Ry = J
25o
45o K

2. Resolving Vectors into Components – the “Vector Collector”
Sketch the vector’s
x & y components
R = J + K
J = 160.km [E25oN]
K = 95.0km [SE]
opp
adj X Y
Jx =
Jy =
Kx =
Ky =
Rx =
Ry = J Jy
25o Jx K Ky
45o Kx

3. Resolving Vectors into Components – the “Vector Collector”
Solve for the vector’s
x & y components
R = J + K
J = 160.km [E25oN]
K = 95.0km [SE]
opp
adj
NOTE: sin 45 = cos 45 (Gotta those triangles!) X Y
Jx = (cos Ѳ) (hyp)
= (cos 25o) (160 km)
= 145 km [E]
Jy = (sin Ѳ) (hyp)
= (sin 25o) (160 km)
= 67.6 km [N]
Kx = (sin Ѳ) (hyp)
= (sin 45o) (95.0 km)
= 67.2km [E]
Ky = (cos Ѳ) (hyp)
= (cos 45o) (95.0 km)
= 67.2km [S]
Rx =
Ry = J Jy
25o Jx K Ky
45o Kx

4. Resolving Vectors into Components – the “Vector Collector”
R = J + K
J = 160.km [E25oN]
K = 95.0km [SE]
opp
adj
adj add all the X’s
to find the total X;
then do the same
for all the Y’s
NOTE: sin 45 = cos 45 (Gotta those triangles!) X Y
Jx = (cos Ѳ) (hyp)
= (cos 25o) (160 km)
= 145 km [E]
Jy = (sin Ѳ) (hyp)
= (sin 25o) (160 km)
= 67.6 km [N]
Kx = (sin Ѳ) (hyp)
= (sin 45o) (95.0 km)
= km [E]
Ky = (cos Ѳ) (hyp)
= (cos 45o) (95.0 km)
= 67.2km [S]
Rx = km [E]
km [E]
212.2 km [E]
212 km [E]
Ry = km [N]
km [S] [N]
0.4 km [N] J Jy
25o Jx K Ky
45o Kx

5. To re-assemble your vector, use pythagorean theorem
R2 = Rx2 + Ry2
= (212)2 + (0.4) red number
= denotes the
R = √ last significant = 212 km [E Ѳ N] figure
tanѲ = Ry so Ѳ = tan-1 Ry
Rx Rx
= tan
212
= 0.1o
•• R = 212 km [E 0.1oN]
Rx = 212 km [E]
Ry = 0.4 km [N] R Rx Ѳ Ry •

6. Now try this one, R = P + Q P = 11.0 m [N27oE] Q = 15.0 m [E25oN]
First step:
Sketch your vectors
(no peaking til
everybody’s given it a try!!) X Y
Px =
Py =
Qx =
Qy =
Rx =
Ry =

7. R = P + Q
P = 11.0 m [N27oE]
Q = 15.0 m [E25oN] X Y
Px =
Py =
Qx =
Qy =
Rx =
Ry = Px Py
27o P Q Qy
Now use the Vector Collector to calculate the components of each vector.
25o Qx

8. R = P + Q
P = 11.0 m [N27oE]
Q = 15.0 m [E25oN] X Y
Px =(sin Ѳ) (hyp)
= (sin 27o) (11.0 m)
= 4.99 m [E]
Py =(cos Ѳ) (hyp)
= (cos 27o) (11.0 m)
= 9.80 m [N]
Qx =(cos Ѳ) (hyp)
= (cos 25o) (15.0 m)
= 13.6 m [E]
Qy =(sin Ѳ) (hyp)
= (sin 25o) (15.0 m)
= 6.34 m [N]
Rx = m [E]
m [E]
18.59 m [E]
= 18.6 m [E]
Ry = m [N]
m [N]
16.14 m [N] Px Py
27o P Q Qy
25o
Now reassemble your resultant vector using the pythagorean theorem. Qx

9. R = P + Q
R2 = Rx2 + Ry2
= (18.6)2 + (16.14)2 =
R = √
= 24.6 m [E Ѳ N]
Ѳ = tan-1 Ry Rx
= tan
18.6
= 40.9o or 41 o
R = 24.6 m [E41oN] X Y
Px =(sin Ѳ) (hyp)
= (sin 27o) (11.0 m)
= 4.99 m [E]
Py =(cos Ѳ) (hyp)
= (cos 27o) (11.0 m)
= 9.80 m [N]
Qx =(cos Ѳ) (hyp)
= (cos 25o) (15.0 m)
= 13.6 m [E]
Qy =(sin Ѳ) (hyp)
= (sin 25o) (15.0 m)
= 6.34 m [N]
Rx = m [E]
m [E]
18.59 m [E]
= 18.6 m [E]
Ry = m [N]
m [N]
16.14 m [N] R Ry Ѳ Rx

10. How would it change if there was subtraction, R = P – Q
How would it change if there was subtraction, R = P – Q ? Think “add the negative” R = P +(–Q)
P = 11.0 m [N27oE]
Q = 15.0 m [E25oN]
-Q = 15.0 m [W25oS]
“-Q” is the new name
For the vector going in
the exact opposite
direction of “Q” X Y
Px =
Py =
-Qx =
-Qy =
Rx =
Ry =

11. R = P + (-Q)
P = 11.0 m [N27oE]
-Q = 15.0 m [W25oS] X Y
Px =(sin Ѳ) (hyp)
= (sin 27o) (11.0 m)
= 4.99 m [E]
Py =(cos Ѳ) (hyp)
= (cos 27o) (11.0 m)
= 9.80 m [N]
-Qx =(cos Ѳ) (hyp)
= (cos 25o) (15.0 m)
= 13.6 m [W]
-Qy =(sin Ѳ) (hyp)
= (sin 25o) (15.0 m)
= 6.34 m [S]
Rx = m [E] [W]
m [W]
8.61 m [W]
= 8.6 m [W]
Ry = m [N]
m [S] [N]
3.46 m [N] Px Py
27o P Q Qy
-Qx
25o
25o
-Qy Qx -Q
Because the directions for -Qx & -Qy have flipped, the resultant components change too!

12. R = P + (-Q) R2 = Rx2 + Ry2 = (8.6)2 + (3.46)2 = 73.96 + 11.9716
= (8.6)2 + (3.46)2 =
R = √
= 9.3 m [W Ѳ N]
Ѳ = tan-1 Ry = tan = 22o
Rx R = 9.3 m [W22oN] X Y
Px =(sin Ѳ) (hyp)
= (sin 27o) (11.0 m)
= 4.99 m [E]
Py =(cos Ѳ) (hyp)
= (cos 27o) (11.0 m)
= 9.80 m [N]
-Qx =(cos Ѳ) (hyp)
= (cos 25o) (15.0 m)
= 13.6 m [W]
-Qy =(sin Ѳ) (hyp)
= (sin 25o) (15.0 m)
= 6.34 m [S]
Rx = m [E] [W]
m [W]
8.61 m [W]
= 8.6 m [W]
Ry = m [N]
m [S] [N]
3.46 m [N] Ry R Rx