Sheet
toc ●
scalar ●
rect polar ●
v addition ●
storage ●
Content
This sheet. Table of Content & notes.
Completes scalar multiplication.
Convert rectangular to polor, or polar to rectangular.
Enter rectangular or polar, yield resultant.
all nomographs and lines
Enter data in yellow. Other colored cells self comp
Completes scalar multiplication and rectangular addition & sub
Enter data in yellow. Other colored cells self compute.
The magnitude of the vector is V and R is the resultant magnitude.
Theta is Θ, the direction of the vector, IN DEGREE NOTATION.
●
Compute the product of scalar m and vector (x,y).
Components x and y are each scaled by m.
This is m(x,y)
the product.
m
x
y
x
y
-3
2
-5
-6
15
●
Compute the product of scalar m and vector r @ Θ degrees.
The magnitude r is scaled by m. The direction Θ remains the same.
This is m(x,y)
the product.
m
r
Θ
r
Θ
-3
4
30
-12
30
If r is negative, one may add 180º to Θ and m
r
Θ
12
210
●
Computes addition of vectors in rectangular notation.
The x-components are added. The y-components are added.
x
y
x
y
x
y
1
2
+
3
4
=
4
6
●
Computes addition of vectors in rectangular notation.
The x-components are added. The y-components are added.
x
y
x
y
x
y
4
5
6
7
=
-2
-2
gular addition & subtraction.
ls self compute.
the resultant magnitude.
DEGREE NOTATION.
s the same.
e may add 180º to Θ and make r positive.
Convert polar to rectangular or rectangular to polar.
Enter data in YELLOW. Other colored cells self compute.
Vector
Magnitude, r
Direction, Θ
x is r*cos(Θ)
y is r*sin(Θ)
A
4
0
4.0000
0.0000
B
5
53.1301023542
3.0000
4.0000
The magnitude of vector V is r and has direction Θ, and rectangular coordinate (x,y).
Theta, Θ, the direction is written IN DEGREE NOTATION.
Add up to 6 vectors to find the resultant vector. Three may be in po
Enter data in yellow. Other colore
The magnitude of the vector is V and R is the resultant magnitude.
Theta is Θ, the direction of the vector, IN DEGREE NOTATION.
Vector Magnitude, V Direction, Θ
x is R*cos(Θ)
y is R*sin(Θ) 1st: Enter magnitude and direction of each
A
0
0
0.0000
0.0000
2nd: These are rewritten in rectangular for
B
4
90
0.0000
4.0000
3rd: Enter the x- and y- components of oth
C
4
270
0.0000
-4.0000
4th: The x-components are added
D
1
0
1.0000
0.0000
5th: The y-components are added.
E
1
180
-1.0000
0.0000
Polar Coordinates are computed though no
F
2.828427125
-135
-2.0000
-2.0000
6th: The magnitude of the resultant is com
Resultant
2.8284
-135
-2.0000
-2.0000
7th: The direction of the resultant is comp
r. Three may be in polar form to begin.
yellow. Other colored cells self compute.
r magnitude and direction of each vector given in polar form.
se are rewritten in rectangular form.
er the x- and y- components of other vectors.
x-components are added
y-components are added.
ordinates are computed though not needed.
magnitude of the resultant is computed. Magnitude is SQRT( [Sum(x)]² + [Sum(y)]² )
direction of the resultant is computed.
Theta is ATAN2( Sum(y) / Sum(x) )*(180/PI()), the arctan of coordinates, and it adjusts for
n of coordinates, and it adjusts for quadrant.
Convert polar to rectangular or rectangular to polar.
Enter data in YELLOW. Other colored cells self compute.
Vector
Magnitude, r
Direction, Θ x is r*cos(Θ) y is r*sin(Θ)
A
4
0
4.0000
0.0000
B
5
53.13010235
3.0000
4.0000
The magnitude of vector V is r and has direction Θ, and rectangular coordinate (x,y).
Theta, Θ, the direction is written IN DEGREE NOTATION.
Add up to 6 vectors to find the resultant vector. Three may be in p
Enter data in yellow. Other colored c
The magnitude of the vector is V and R is the resultant magnitude.
Theta is Θ, the direction of the vector, IN DEGREE NOTATION.
Vector Magnitude, V Direction, Θ
x is R*cos(Θ) y is R*sin(Θ) 1st: Enter magnitude and direction of each vector g
A
0
0
0.0000
0.0000
2nd: These are rewritten in rectangular form.
B
4
90
0.0000
4.0000
3rd: Enter the x- and y- components of other vecto
C
D
E
F
Resultant
4
1
1
2.828427
2.8284
270
0
180
-135
-135
0.0000
1.0000
-1.0000
-2.0000
-2.0000
-4.0000
0.0000
0.0000
-2.0000
-2.0000
4th: The x-components are added
5th: The y-components are added.
Polar Coordinates are computed though not neede
6th: The magnitude of the resultant is computed.
7th: The direction of the resultant is computed.
Completes scalar multiplicati
Enter data in yellow. Ot
compute.
The magnitude of the v
Theta is Θ, the directio
●
Compute the product of scalar m and
Components x and y are each scaled
m
-3
●
Three may be in polar form to begin.
. Other colored cells self compute.
and direction of each vector given in polar form.
ten in rectangular form.
y- components of other vectors.
ts are added
ts are added.
computed though not needed.
f the resultant is computed.
he resultant is computed.
r
4
Θ
30
Computes addition of vectors in recta
The x-components are added. The yx
1
●
y
-5
Compute the product of scalar m and
The magnitude r is scaled by m. The d
m
-3
●
x
2
y
2
+
Computes addition of vectors in recta
The x-components are added. The yx
y
4
5
Magnitude is SQRT( [Sum(x)]² + [Sum(y)]² )
Theta is ATAN2( Sum(y) / Sum(x) )*(180/PI()), the arctan of coordinates, and it adjusts for quadran
Save your own copy first.
Enter data in blue cells.
The yellow cells self compute.
scalar multiplication and rectangular addition & subtraction.
r data in yellow. Other colored cells self compute.
The magnitude of the vector is V and R is the resultant magnitude.
Theta is Θ, the direction of the vector, IN DEGREE NOTATION.
product of scalar m and vector (x,y).
x and y are each scaled by m.
This is m(x,y)
the product.
x
y
-6
15
product of scalar m and vector r @ Θ degrees.
e r is scaled by m. The direction Θ remains the same.
This is m(x,y)
the product.
r
Θ
-12
30
If r is negative, one may add 180º to Θ and make r positive.
r
Θ
12
210
dition of vectors in rectangular notation.
nents are added. The y-components are added.
x
3
y
4
=
x
4
y
6
dition of vectors in rectangular notation.
nents are added. The y-components are added.
x
y
x
y
6
7
=
-2
-2