Question 1
Instructions: On occasion, the notation
= [A, θ] will be a shorthand notation for
.
Given two non-zero vectors,
![](data:image/png;base64, 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)
and
![](data:image/png;base64, iVBORw0KGgoAAAANSUhEUgAAAA0AAAAYCAIAAACukuADAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAC7SURBVDhPpZDbEcMgDATpgBJSAv1XQQmUQAlk8cmCYJI4k/1ghLRzPEK7x99erdWqg+7RWiilpJRYqYdH63EhhMDKSOoveVvcEG+9hY23JInVQ9LNbH+yehgxRl766X7M9COoS+SLx0yePm+OHJ5ulnMmTJF7jzC9YHu0eQrTgFWR89HDo4tB4d4caR57PEfeHNk9P5RCXCO7pzDthXuKpGMVXSJJosVKTcfpkgaiRx3Y/oSOveMr97zWnh/f4gQizluWAAAAAElFTkSuQmCC)
, such that
![](data:image/png;base64, iVBORw0KGgoAAAANSUhEUgAAAA0AAAAYCAIAAACukuADAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAC7SURBVDhPpZDbEcMgDATpgBJSAv1XQQmUQAlk8cmCYJI4k/1ghLRzPEK7x99erdWqg+7RWiilpJRYqYdH63EhhMDKSOoveVvcEG+9hY23JInVQ9LNbH+yehgxRl766X7M9COoS+SLx0yePm+OHJ5ulnMmTJF7jzC9YHu0eQrTgFWR89HDo4tB4d4caR57PEfeHNk9P5RCXCO7pzDthXuKpGMVXSJJosVKTcfpkgaiRx3Y/oSOveMr97zWnh/f4gQizluWAAAAAElFTkSuQmCC)
, the sum
![](data:image/png;base64, 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)
satisfies
◦
![](data:image/png;base64, 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)
.
◦
![](data:image/png;base64, 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)
.
◦
![](data:image/png;base64, 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)
.
◦
![](data:image/png;base64, iVBORw0KGgoAAAANSUhEUgAAAIQAAAAoCAIAAACw+MVlAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAPASURBVGhD7ZfbldswDETdQUrYElyC+/9yCVuCS3CuNDTMBR+iXwpylvdDhwKHAxCIHe/hOgnDHEYg5jACsdMwLpdLWoUkSHl7DIOrHo/HsPOIU95Ow/j6+oo8jCDlhRvGR5tSNX+ovI/yL4dBxPH9/c03Bk/WSfQsMsxpmfP624fBK60h7jgcDjxf/BJ/yJw1wVfSvYv5yZjDaPPRplTNHyrvo4Qbxv78H8N4V32Dt31jO7DqkEQ3iLx3GGuSRAq1yTXNYegbdsRuE0w2b8uuvtDT+wvIiox/brC2VxYuy0h546hvSlfmcrgm14chEXZvKXHktmRU9e/KKEN+PvFkDZjzqh9UeZaR8gYhy+l0ytN1nNG4JleGwR6i8/n8RIlVPcG+lQSUrsalaJfNwhDYMCTG2UWEsm8alrgjvGoSelU6l8sgWDa5MgxNjOdDJaLkCNWUR4j0rZSLNsFIUgRU2JexSyPy1qs7ZQrWD90UEFcv62yXUTSGwfGyyX4YbEjEYrBENLLWwRTN6FsR5yD/RtSpVvU5fUPBrhlSFXBEk3BFjrgZyDjeuayhAqrORHScRS7ww1Amtp2uCrt5ZS1x30oOPNFY79Jeg76hYFfD0ADMnKknxY0RN0AwcllDN6reRT44QJ76xzAkoly25WU6hwRrYduVsduyIigH1jzVvo5YqDblFUmRQVBumq6OyJx1Eq2gbGUUbHFk8LJCnlVbWVWbfB+GzlP6arLAuvQCgqoMR3exKnJuWbGlG/LM25cUN5R0rWtBbRXES3Mi5qZd8+dIrmftIjnE17uOXlag5Ej1FuSijKXuFSsP7sOw8+wBC6Smc0iwFvnSJ0NZDDWr7JcgInRKeUVSZBCUm922jAjW1XQGW+OXBTT5z6pcLx+ZAIs8dRqGOw8o+iWC7DarbFkRySsD1tavvBgHypHaXOvN3J0dcQMEOGxeVhp9C9kRiVn3m7wMw84rBHJBl59sYSmhqncpRTUFa/VLLau6QdUwR+Y2DNbAkartpluOnFuXtSwkNZQRONJvcro2Z5CqIJ6sXXATWQ/+ncG6TKHgUv6NVnYpq1ugXZkL1nrlaTc30BNvuVVBXF5WeZXRwJkBWD1WtsQuuHwyWInFciW9r6TQGFU9wfK2i/WNFPoZFGmjoLMFOlslKTIIPjoMUR5ZEhS4uJSQ3lcUuf8H/jlI9txt9yFOeXMYcxiRmMMIxBxGIOYwAjGHEYg5jEDMYQTi1w3D/uIPSJzy9hgGhJ2ECFLeTsOYjDCHEYg5jDBcr38B4qdG8HibXw8AAAAASUVORK5CYII=)
.
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![](data:image/png;base64, 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)
.
Question 2
Instructions: On occasion, the notation
= [A, θ] will be a shorthand notation for
.
The vector
![](data:image/png;base64, iVBORw0KGgoAAAANSUhEUgAAAA0AAAAYCAIAAACukuADAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAC7SURBVDhPpZDbEcMgDATpgBJSAv1XQQmUQAlk8cmCYJI4k/1ghLRzPEK7x99erdWqg+7RWiilpJRYqYdH63EhhMDKSOoveVvcEG+9hY23JInVQ9LNbH+yehgxRl766X7M9COoS+SLx0yePm+OHJ5ulnMmTJF7jzC9YHu0eQrTgFWR89HDo4tB4d4caR57PEfeHNk9P5RCXCO7pzDthXuKpGMVXSJJosVKTcfpkgaiRx3Y/oSOveMr97zWnh/f4gQizluWAAAAAElFTkSuQmCC)
has components +5 and +7 along the
x and
y axes respectively. If the vector is now rotated 90 degrees counterclockwise relative to the original axes, the vector's components are now
◦
−7; −5.
◦
7; −5.
◦
−7; 5.
◦
7; 5.
◦
7; 0.