Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.
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Transcript of Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.
![Page 1: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/1.jpg)
Vector Addition
Cummutative Law
A
B
CB
A
C
A + B = C B + A = C
A + B = B + A
![Page 2: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/2.jpg)
Vector AdditionAssociative Law
A
B
C
A + B
(A +
B) +
C
A
B
C
B +
C
AA
+ (B
+ C
)
![Page 3: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/3.jpg)
Vector SubtractionSubtract B from A
A
B
-B
A+B
A-B
![Page 4: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/4.jpg)
Right Hand RuleE, B, F
![Page 5: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/5.jpg)
Right Hand Rule
E, B, F
![Page 6: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/6.jpg)
Right Hand Rule
Right Hand Rule for “F”
Fingers in the direction of B. Thumb in the direction of I. Palm in the direction of F.
![Page 7: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/7.jpg)
Right Hand Rule
Right hand rule for force:
Fingers in the direction of B. Thumb in the direction of I. Palm in the direction of F.
![Page 8: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/8.jpg)
Right Hand Rule
What happens when a current is driven through the wire?
Force out of the screen. Force into the screen.
![Page 9: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/9.jpg)
Resolution of Vector
Orthogonal Vectors
A
x
z
y
^
^ ^
ZY
YX
XZZYX
![Page 10: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/10.jpg)
Resolution of Vector
Component Vectors
A = Ax + Ay + Az
A = xAx + yAy + zAz^ ^ ^
|A| =√Ax2 + Ay
2 + Az2
![Page 11: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/11.jpg)
Vector Problems 1:
1. A = x6 + y3 B = x4 - y7^ ^ ^ ^
A + B = ?
Magnitude of Resulting Vector ?
Its angle with respect to x- axis ?
![Page 12: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/12.jpg)
Solution of Problem 1
Unit Vectors x (6+4) =10
Unit Vectors y (3-7) = -4
Magnitude of Resultant Vector C=√102 + (-4)2
= √116 = 10.8
Angle α =tan-1 (-4/10) = -21.8º
![Page 13: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/13.jpg)
Vector Problem 2:
Addition of Three Vectors
A = -x8 + y12; B = -x5 + y15; C = x7 – y9
Magnitude of Resultant Vector D ?
Angle of D with x-axis ?
![Page 14: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/14.jpg)
Scalar Product
Product of their magnitudes
multiplied by the cosine of the
angle between the Vectors
Scalar / Dot Product of Two Vectors
![Page 15: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/15.jpg)
Orthogonal Vectors
Angular Dependence
![Page 16: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/16.jpg)
Scalar Product
Scalar Product of a Vector with itself ?
A . A = |A||A| cos 0º
= A2
![Page 17: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/17.jpg)
Scalar Product
Scalar Product of a Vector and Unit vector ?
x . A =|x||A|cosα
= Ax
Yields the component of a vector in a direction of the unit
vector
Where alpha is an angle between A and unit vector x
^ ^
![Page 18: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/18.jpg)
Scalar Product
Scalar Product of Rectangular Coordinate
Unit vectors?
x.y = y.z = z.x = ?
= 0
x.x = y.y = z.z = ?
= 1
![Page 19: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/19.jpg)
Scalar Product Problem 3:
A . B = ?
( hint: both vectors have components in three directions of unit vectors)
![Page 20: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/20.jpg)
Scalar Product Problem 4:A = y3 + z2;B= x5 + y8
A . B = ?
![Page 21: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/21.jpg)
Scalar Product Problem 5:
A = -x7 + y12 +z3;
B = x4 + y2 + z16
A.B = ?
![Page 22: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/22.jpg)
Cylindrical Coordinates
r =
=
z = z
![Page 23: Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649ecb5503460f94bd9aa9/html5/thumbnails/23.jpg)
Spherical Coordinates
=
=
=
x = r sin cos
y = r sin sin
z = r cos