# Khan/khan-exercises

Switch branches/tags
Nothing to show
Fetching contributors…
Cannot retrieve contributors at this time
297 lines (266 sloc) 15.4 KB
 Scaling vectors
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(max(-9, -9 - AX), min(9, 9 - AX)) randRangeNonZero(max(-9, -9 - AY), min(9, 9 - AY)) randRangeNonZero(max(-9, -9 - BX), min(9, 9 - BX)) randRangeNonZero(max(-9, -9 - BY), min(9, 9 - BY)) randRangeNonZero(max(-9, -9 - CX), min(9, 9 - CX)) randRangeNonZero(max(-9, -9 - CY), min(9, 9 - CY)) randRangeNonZero(max(-9, -9 - DX), min(9, 9 - DX)) randRangeNonZero(max(-9, -9 - DY), min(9, 9 - DY)) randRangeNonZero(max(-9, -9 - EX), min(9, 9 - EX)) randRangeNonZero(max(-9, -9 - EY), min(9, 9 - EY)) 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() { line( [AOX, AOY], [AOX + AX, AOY + AY], { arrows: "->" } ); label( [AOX + AF * AX, AOY + AF * AY], "\\vec a" ); }); style({ stroke: PINK, color: PINK }, function() { line( [BOX, BOY], [BOX + BX, BOY + BY], { arrows: "->" } ); label( [BOX + BF * BX, BOY + BF * BY], "\\vec b" ); }); style({ stroke: GREEN, color: GREEN }, function() { 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.

randRangeNonZero(-8, 8) randRangeNonZero(-8, 8) randFromArray([-1, -0.5, 0.5, -2, 2, -3, 3, -4, 4, -5, 5])

\vec a = AX \hat\imath + AY \hat\jmath.

What is -\vec a?

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

AX * SA \hat\imath + {} AY * SA \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

randRangeNonZero(-8, 8) randRangeNonZero(-8, 8) randFromArray([-1, -0.5, 0.5, -2, 2, -3, 3, -4, 4, -5, 5])

\vec a = (AX, AY)

What is -\vec a?

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

-\vec adecimalFraction(SA, true) \vec a = ( AX * SA, AY * SA)

SA \vec a = SA \cdot (AX, AY)

\hphantom{SA \vec a} = (SA \cdot AX, SA \cdot AY)

\hphantom{SA \vec a} = (SA * AX, SA * AY)

randFromArray([-1, -0.5, 0.5, -2, 2, -0.25, 0.25, -4, 4])
abs(SA) < 1 ? randRangeNonZero(-4, 4) * 2 : randRangeNonZero(-4, 4) / 2 abs(SA) < 1 ? randRangeNonZero(-4, 4) * 2 : randRangeNonZero(-4, 4) / 2
1 + 0.8 / sqrt(AX * AX + AY * AY) 1 + 0.8 / (abs(SA) * sqrt(AX * AX + AY * AY)) [[AX], [AY]] randFromArray([ AX + "\\hat\\imath + " + AY + "\\hat\\jmath", "(" + AX + ", " + AY + ")" ]) i18n._("against") i18n._("along") i18n._("positive") i18n._("negative") ["", AGAINST, ALONG] SA < 0 ? AGAINST : ALONG SA < 0 ? NEGATIVE : POSITIVE

\vec a = FORMAT

\vec b = -\vec a

\vec b = decimalFraction(SA, true) \vec a

What is the magnitude and direction of \vec b compared to \vec a?

\vec b is abs(SA) times the size of \vec a.
\vec b moves SOLUTION \vec a.

graphInit({ range: 10, scale: 20, tickStep: 1, axisArrows: "<->" }); style({ stroke: BLUE, color: BLUE }, function() { line([0, 0], [AX, AY], { arrows: "->" } ); label([AF * AX, AF * AY], "\\vec a" ); });
style({ strokeDasharray: ".", color: BLACK }, function() { line([0, 0], [AX * SA, AY * SA], { arrows: "->" } ); label([BF * AX * SA, BF * AY * SA], "\\vec b" ); });

\vec a is scaled by SA to create vector \vec b.

SA is SIGN, so the direction of \vec b is SOLUTION \vec a.

Each of the components of \vec a is multiplied by SA to get \vec b, so the magnitude of \vec b is abs(SA) times the size of \vec a.