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VECTOR ANALYSIS FOR ELECTROMAGNETISM - Coggle Diagram
VECTOR ANALYSIS FOR ELECTROMAGNETISM
WHAT IS VECTOR ?
A QUANTITY THAT HAS BOTH MAGNITUDE AND DIRECTION
A SCALAR IS A QUANTITY THAT HAS ONLY MAGNITUDE
A FIELD IS A FUNCTION THAT SPECIFIES A PARTICULAR QUANTITY EVERYWHERE IN A REGION
IT IS CUSTOMARY TO REPRESENT A VECTOR BY A LETTER WITH AN ARROW ON TOP OF IT .
UNIT VECTOR
RULES FOR VECTOR ADDITION AND SUBTRACTION
VECTOR ADDITION
PARALLELOGRAM RULE
HEAD-TO-TAIL RULE
VECTOR SUBTRACTION
HEAD-TO-TAIL RULE
PARALLELOGRAM RULE
3 BASIC LAWS OF ALGEBRA
COMMUTATIVE
ASSOCIATIVE
DISTRIBUTIVE
POSITION VECTOR
DISTANCE VECTOR @ DISPLACEMENT VECTOR
IS THE DISPLACEMENT FROM ONE POINT TO ANOTHER
DOT PRODUCT @ SCALAR PRODUCT
TWO VECTORS A and B ARE SAID TO BE ORTHOGONAL (OR PERPENDICULAR) WITH EACH OTHER
SOME BASIC PROPERTIES OF DOT PRODUCTS
COMMUTATIVE LAW
DISTRIBUTIVE LAW
ALSO NOTE THAT ....
CROSS PRODUCT @ VECTOR PRODUCT
VECTOR QUANTITY
MAGNITUDE IS THE AREA OF THE PARALLELOPIPED
DIRECTION OF ADVANCE OF A RIGHT-HANDED SCREW
THE xyz PERMUTATION FOR CROSS PRODUCT TERMS
SOME BASIC PROPERTIES OF CROSS PRODUCTS
IT IS NOT COMMUTATIVE
IT IS ANTICOMMUTATIVE
IT IS NOT ASSOCIATIVE
IT IS DISTRIBUTIVE
ALSO NOTE THAT ....
TRIPLE PRODUCTS
SCALAR TRIPLE PRODUCT
VECTOR TRIPLE PRODUCT
COMPONENTS OF VECTOR
IS THE PROJECTION OF THE VECTOR IN A GIVEN DIRECTION
SCALAR COMPONENT
VECTOR COMPONENT