randRangeNonZero( -3, 3 ) randRangeNonZero( -3, 3 ) randFromArray([-1, -0.5, 0.5, -2, 2, -3, 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", "pink"], ["c", "green"], ["d", "purple"], ["e", "red"] ][ $.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 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) 1 + 0.8 / sqrt( AX * AX + AY * AY ) 1 + 0.8 / sqrt( BX * BX + BY * BY ) 1 + 0.8 / sqrt( CX * CX + CY * CY ) 1 + 0.8 / sqrt( DX * DX + DY * DY ) 1 + 0.8 / sqrt( EX * EX + EY * EY )

What is -\vec a?

What is decimalFraction(SA, true) \vec a?

graphInit({ range: 10, scale: 20, tickStep: 1, axisArrows: "<->" }); style({ stroke: BLUE, color: BLUE }, function() { var AF = 1 + 0.8 / sqrt( AX * AX + AY * AY ); line( [AOX, AOY], [AOX + AX, AOY + AY], { arrows: "->" } ); label( [AOX + AF * AX, AOY + AF * AY], "\\vec a" ); }); style({ stroke: PINK, color: PINK }, 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: GREEN, color: GREEN }, 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: PURPLE, color: PURPLE }, function() { line( [DOX, DOY], [DOX + DX, DOY + DY], { arrows: "->" } ); label( [DOX + DF * DX, DOY + DF * DY], "\\vec d" ); }); style({ stroke: RED, color: RED }, function() { line( [EOX, EOY], [EOX + EX, EOY + EY], { arrows: "->" } ); label( [EOX + EF * EX, EOY + EF * EY], "\\vec e" ); });

\large\ANSC{\vec ANSL}

  • \large\pink{\vec b}
  • \large\green{\vec c}
  • \large\purple{\vec d}
  • \large\red{\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.