MATM1544_lecture 16 (2).pdf - The image part with relationship ID rId7 was not found in the file MATM1544 LECTURE 16 Scalar multiplication and vector

MATM1544_lecture 16 (2).pdf - The image part with...

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8/14/2015 1 The image part with relationship ID rId7 was not found in the file. T: +27(0)51 401 9111 | [email protected] | MATM1544 LECTURE 16 Scalar multiplication and vector components August 14, 2015 T: 051 401 9111 [email protected] CONTENT Multiplying by a scalar Vector components Examples Exercises
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8/14/2015 2 When adding two vectors along the same line, the triangle collapses into a single line: The vector ° + ± now has magnitude ° + ± , i.e. we simply add the two magnitudes together if the two point in the same direction. MULTIPLYING BY A SCALAR Adding ° to itself: The vector has magnitude 2°, and is in the same direction as ° .
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8/14/2015 3 In general we have the rule When a vector ² is multiplied by a scalar ³, the vector ³° has as magnitude the magnitude of ° times ³ , i.e. ³ °. If ³ > 0, then ³° is in the same direction as ° . If ³ < 0, then ³° is in the opposite direction than ° . e.g. −0,5° is in the opposite direction than ° Magnitude is |-0,5|=0,5 times that of ° . VECTOR COMPONENTS Components of ° : Two vectors which add up to ° . ° ´ and ° µ are components of °
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8/14/2015 4 Components are not unique: Use rectangular components: Choose - axis and · - axis
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