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Published byMelanie McDaniel Modified over 9 years ago
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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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Vector Addition Associative Law A B C A + B (A + B) + C A B C B + C A A + (B + C)
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Vector Subtraction Subtract B from A A B -B A+B A-B
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Right Hand Rule E, B, F
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Right Hand Rule E, B, F
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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.
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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.
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Right Hand Rule What happens when a current is driven through the wire? Force out of the screen.Force into the screen.
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Resolution of Vector Orthogonal Vectors A x z y ^ ^^ ZY YX XZ ZYX
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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
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Vector Problems 1: 1.A = x6 + y3B = x4 - y7 ^^^^ A + B = ? Magnitude of Resulting Vector ? Its angle with respect to x- axis ?
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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
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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 ?
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Scalar Product Product of their magnitudes multiplied by the cosine of the angle between the Vectors Scalar / Dot Product of Two Vectors
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Orthogonal Vectors Angular Dependence
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Scalar Product Scalar Product of a Vector with itself ? A. A = | A || A | cos 0 º = A 2
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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 ^^
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Scalar Product Scalar Product of Rectangular Coordinate Unit vectors? x.y = y.z = z.x = ? = 0 x.x = y.y = z.z = ? = 1
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Scalar Product Problem 3: A. B = ? ( hint: both vectors have components in three directions of unit vectors)
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Scalar Product Problem 4: A = y3 + z2;B= x5 + y8 A. B = ?
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Scalar Product Problem 5: A = -x7 + y12 +z3; B = x4 + y2 + z16 A.B = ?
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Cylindrical Coordinates r =r = = z = z
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Spherical Coordinates = = = x = r sin cos y = r sin sin z = r cos
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