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Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.

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Presentation on theme: "Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A."— Presentation transcript:

1 Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A

2 Vector Addition Associative Law A B C A + B (A + B) + C A B C B + C A A + (B + C)

3 Vector Subtraction Subtract B from A A B -B A+B A-B

4 Right Hand Rule E, B, F

5 Right Hand Rule E, B, F

6 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.

7 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.

8 Right Hand Rule What happens when a current is driven through the wire? Force out of the screen.Force into the screen.

9 Resolution of Vector Orthogonal Vectors A x z y ^ ^^ ZY YX XZ ZYX

10 Resolution of Vector Component Vectors A = A x + A y + A z A = xA x + yA y + zA z ^^^ |A| =√A x 2 + A y 2 + A z 2

11 Vector Problems 1: 1.A = x6 + y3B = x4 - y7 ^^^^ A + B = ? Magnitude of Resulting Vector ? Its angle with respect to x- axis ?

12 Solution of Problem 1 Unit Vectors x  (6+4) =10 Unit Vectors y  (3-7) = -4 Magnitude of Resultant Vector C=√10 2 + (-4) 2 = √116 = 10.8 Angle α =tan -1 (-4/10) = -21.8º

13 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 ?

14 Scalar Product Product of their magnitudes multiplied by the cosine of the angle between the Vectors Scalar / Dot Product of Two Vectors

15 Orthogonal Vectors Angular Dependence

16 Scalar Product Scalar Product of a Vector with itself ? A. A = | A || A | cos 0 º = A 2

17 Scalar Product Scalar Product of a Vector and Unit vector ? x. A = | x || A | cosα = A x Yields the component of a vector in a direction of the unit vector Where alpha is an angle between A and unit vector x ^^

18 Scalar Product Scalar Product of Rectangular Coordinate Unit vectors? x.y = y.z = z.x = ? = 0 x.x = y.y = z.z = ? = 1

19 Scalar Product Problem 3: A. B = ? ( hint: both vectors have components in three directions of unit vectors)

20 Scalar Product Problem 4: A = y3 + z2;B= x5 + y8 A. B = ?

21 Scalar Product Problem 5: A = -x7 + y12 +z3; B = x4 + y2 + z16 A.B = ?

22 Cylindrical Coordinates r =r = = z = z

23 Spherical Coordinates = = = x = r sin  cos  y = r sin  sin  z = r cos 


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