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?
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 + ")"
])
$._("against")
$._("along")
$._("positive")
$._("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.