ααααံုးα‘ေααဲα Maths portion αို αα္ေαးαိုα္αါαα္။
Chapter (10) - Introduction to Vectors and Transformation Geometry
αα½ြα္ေαာ္αိုα ေααα
α₯္ααံဳေαြα ααဲ့ physical quantity ေαြαွာ scalar quantity αဲα vector quantity αα္αိုαΏαီး ႏွα
္α်ိဳးαွိαါαα္။
Scalar quantity ေαြαွာα α‘αိုα္းα‘αာ (magnitude) αာαွိαါαα္။ Vector quantity ေαြαွာေαာ့ α‘αိုα္းα‘αာαဲα α₯ီးαα္αာ (magnitude and direction) αα္αိုαΏαီးႏွα ္α်ိဳးαွိαါαα္။
A scalar is a simple physical quantity that is not changed by coordinate system rotations or translations(defined by Wikipedia)
Examples of scalar quantities
* electric charge and charge density
* mass and mass density
* speed, but not velocity or momentum
* temperature
* energy and energy density
* time
* pressure
* entropy
* negentropy
In elementary mathematics, physics, and engineering, a vector (sometimes called a geometric or spatial vector) is a geometric object that has both a magnitude (or length), direction and sense that is orientation along the given direction. A vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by
α‘αိုα္းα‘αာαိုαာα α‘αြα္ααူ αိαာαα္αွားα ြာ ေαြαျαα္ႏိုα္αါαα္။ αိုαေαာ္ α‘α်ိဳαေαာ quantity ေαြαွာ α‘αိုα္းα‘αာααာα (magnitude) ေျαာα္းαဲျαα္းααွိေαာ္αα္း α₯ီးαα္αာေျαာα္းαα္း αႈေαΎαာα့္ ααα္ေαြ ေျαာα္းαဲαါαα္။
α‘ဲαါေαြαေαာ့ vector quantity ေαြαဲျαα ္αါαα္။ vector quantity ေαြαို resolve αုα္αိုα geometry αိုα‘αံုးα် ေျααွα္းႏိုα္αါαα္။
αီα‘αα္းαေαာ့ vector αဲ့ base concept and theory αို α αα္αိα္αα္ေαးျαα္းαာ ျαα ္αါαα္။ αα္ေαြα α‘αံုးα်ေျααွα္းαα္းα်ားαိုေαာ့ ααၠαိုα္္αα္း α်ားαွာαα္αα္αα္αΎαားαွာျαα ္αါαα္။
ေα်ာα္းαား/αူ α‘ေαာ္α်ားα်ား αီα‘αα္းαို αα္αα ္αα္αΎααါαα္။ αိααΈံαာαာαြဲα်ားαို ααၠαိုα္αွာ αα္αα္ ေα့αာαα္αူαိုα αα္αြα္αားαα္ (αα္αၤ်ာ αာαာαα္ႏွα့္ ααα္းαြာαေαြα) αီα‘αα္းαို α‘αူးαိαွိαားαα္αားαိုα αိုα‘α္αါေαΎαာα္း α‘ααံျαဳαါαေα ။
αααα₯ီးαံုးα‘ေααဲα Section (10.1) Geometric vectors αဲ့ αားαα္αားααα့္ definition α်ားαဲα αွα္းαα္းα်α္α်ား၊ αုုα ၧာα‘α်ိဳαα ႏွα့္ ေျααွα္းαံုα်ား (Problems and Answers) α်ားαို αα္ျαေαးαိုα္αါαα္။
α်α္αွိေααဲ့ section αα္းαα္αα္ αα္ေαးαြားαါ့αα္။ ေα်ာα္းαားαူα်ားα‘ားαံု αူးαα½ြα္αα္ျαα္α ြာ αααα္းαိုα္α‘αα့္αα့္αို ေα်ာ္αြα္ ျαα္αα္းႏိုα္αါေα ။
Chappter-10(Section-1) DOWNLOAD
Chappter-10(Section-1_Problems and Answers) DOWNLOAD
Scalar quantity ေαြαွာα α‘αိုα္းα‘αာ (magnitude) αာαွိαါαα္။ Vector quantity ေαြαွာေαာ့ α‘αိုα္းα‘αာαဲα α₯ီးαα္αာ (magnitude and direction) αα္αိုαΏαီးႏွα ္α်ိဳးαွိαါαα္။
A scalar is a simple physical quantity that is not changed by coordinate system rotations or translations(defined by Wikipedia)
Examples of scalar quantities
* electric charge and charge density
* mass and mass density
* speed, but not velocity or momentum
* temperature
* energy and energy density
* time
* pressure
* entropy
* negentropy
In elementary mathematics, physics, and engineering, a vector (sometimes called a geometric or spatial vector) is a geometric object that has both a magnitude (or length), direction and sense that is orientation along the given direction. A vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by
α‘αိုα္းα‘αာαိုαာα α‘αြα္ααူ αိαာαα္αွားα ြာ ေαြαျαα္ႏိုα္αါαα္။ αိုαေαာ္ α‘α်ိဳαေαာ quantity ေαြαွာ α‘αိုα္းα‘αာααာα (magnitude) ေျαာα္းαဲျαα္းααွိေαာ္αα္း α₯ီးαα္αာေျαာα္းαα္း αႈေαΎαာα့္ ααα္ေαြ ေျαာα္းαဲαါαα္။
α‘ဲαါေαြαေαာ့ vector quantity ေαြαဲျαα ္αါαα္။ vector quantity ေαြαို resolve αုα္αိုα geometry αိုα‘αံုးα် ေျααွα္းႏိုα္αါαα္။
αီα‘αα္းαေαာ့ vector αဲ့ base concept and theory αို α αα္αိα္αα္ေαးျαα္းαာ ျαα ္αါαα္။ αα္ေαြα α‘αံုးα်ေျααွα္းαα္းα်ားαိုေαာ့ ααၠαိုα္္αα္း α်ားαွာαα္αα္αα္αΎαားαွာျαα ္αါαα္။
ေα်ာα္းαား/αူ α‘ေαာ္α်ားα်ား αီα‘αα္းαို αα္αα ္αα္αΎααါαα္။ αိααΈံαာαာαြဲα်ားαို ααၠαိုα္αွာ αα္αα္ ေα့αာαα္αူαိုα αα္αြα္αားαα္ (αα္αၤ်ာ αာαာαα္ႏွα့္ ααα္းαြာαေαြα) αီα‘αα္းαို α‘αူးαိαွိαားαα္αားαိုα αိုα‘α္αါေαΎαာα္း α‘ααံျαဳαါαေα ။
αααα₯ီးαံုးα‘ေααဲα Section (10.1) Geometric vectors αဲ့ αားαα္αားααα့္ definition α်ားαဲα αွα္းαα္းα်α္α်ား၊ αုုα ၧာα‘α်ိဳαα ႏွα့္ ေျααွα္းαံုα်ား (Problems and Answers) α်ားαို αα္ျαေαးαိုα္αါαα္။
α်α္αွိေααဲ့ section αα္းαα္αα္ αα္ေαးαြားαါ့αα္။ ေα်ာα္းαားαူα်ားα‘ားαံု αူးαα½ြα္αα္ျαα္α ြာ αααα္းαိုα္α‘αα့္αα့္αို ေα်ာ္αြα္ ျαα္αα္းႏိုα္αါေα ။
Chappter-10(Section-1) DOWNLOAD
Chappter-10(Section-1_Problems and Answers) DOWNLOAD
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