# Khan/khan-exercises

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 Scaling vectors
randRangeNonZero( -3, 3 ) randRangeNonZero( -3, 3 ) randRangeNonZero( -1, 1 ) * randRange( 2, 3 ) randRangeNonZero( -7, 7 ) randRangeNonZero( -7, 7 ) randRangeNonZero( -7, 7 ) randRangeNonZero( -7, 7 ) AX * SA AY * SA -AX * SA -AY * SA [DX, DY] shuffle([ [BX, BY], [CX, CY], ANS, [EX, EY] ]) [ ["b", "#ff00af"], ["c", "#28ae7b"], ["d", "#ffa500"], ["e", "#fd0000"] ][ jQuery.inArray( ANS, SHUF ) ] SHUF[0] SHUF[1] SHUF[2] SHUF[3] randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 )

What is SA \vec a?

graphInit({ range: 10, scale: 20, tickStep: 1, axisArrows: "<->" }); style({ stroke: "#6495ed", color: "#6495ed" }, function() { var AF = 1 + 0.8 / sqrt( AX * AX + AY * AY ); do { var AOX = randRange( -9, 9 ); var AOY = randRange( -9, 9 ); } while ( 0 < abs( AOX + AX ) && abs( AOX + AX ) < 9 ); line( [0, 0], [AX, AY], { arrows: "->" } ); label( [AF * AX, AF * AY], "\\vec a" ); }); style({ stroke: "#ff00af", color: "#ff00af" }, function() { var BF = 1 + 0.8 / sqrt( BX * BX + BY * BY ); line( [BOX, BOY], [BOX + BX, BOY + BY], { arrows: "->" } ); label( [BOX + BF * BX, BOY + BF * BY], "\\vec b" ); }); style({ stroke: "#28ae7b", color: "#28ae7b" }, function() { var CF = 1 + 0.8 / sqrt( CX * CX + CY * CY ); line( [COX, COY], [COX + CX, COY + CY], { arrows: "->" } ); label( [COX + CF * CX, COY + CF * CY], "\\vec c" ); }); style({ stroke: "#ffa500", color: "#ffa500" }, function() { var DF = 1 + 0.8 / sqrt( DX * DX + DY * DY ); line( [DOX, DOY], [DOX + DX, DOY + DY], { arrows: "->" } ); label( [DOX + DF * DX, DOY + DF * DY], "\\vec d" ); }); style({ stroke: "#fd0000", color: "#fd0000" }, function() { var EF = 1 + 0.8 / sqrt( EX * EX + EY * EY ); line( [EOX, EOY], [EOX + EX, EOY + EY], { arrows: "->" } ); label( [EOX + EF * EX, EOY + EF * EY], "\\vec e" ); });

\vec ANSL

• \vec b
• \vec c
• \vec d
• \vec e

Reading from the graph, we see that \vec a = AX \hat\imath + AY \hat\jmath.

SA \vec a = SA \cdot (AX \hat\imath + AY \hat\jmath).

\hphantom{SA \vec a} = (SA \cdot AX) \hat\imath + (SA \cdot AY) \hat\jmath.

\hphantom{SA \vec a} = SA * AX \hat\imath + SA * AY \hat\jmath.

The vector that matches is \vec ANSL.

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