randRangeNonZero(-5, 5) randRangeNonZero(-5, 5) randRange(0, 1) ["x", "y"][COMPONENT] $._("horizontally") $._("vertically") [HORIZONTAL, VERTICAL][COMPONENT] COMPONENT ? randRange(-5, 5) : AX COMPONENT ? AY : randRange(-5, 5) COMPONENT ? randRange(-5, 5) : -AX COMPONENT ? -AY : randRange(-5, 5) COMPONENT ? randRangeNonZero(-5, 5) : randRangeExclude(-5, 5, [AX]) COMPONENT ? randRangeExclude(-5, 5, [AY]) : randRangeNonZero(-5, 5) 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)) COMPONENT ? randRange(-9, -9) : AOX COMPONENT ? AOY : randRange(-9, -9) COMPONENT ? randRangeNonZero(-5, 5) : randRangeExclude(-5, 5, [AX]) COMPONENT ? randRangeExclude(-5, 5, [AY]) : randRangeNonZero(-5, 5) [BX, BY, BOX, BOY] shuffle([ANS, [CX, CY, COX, COY], [DX, DY, DOX, DOY], [EX, EY, EOX, EOY]]) $.inArray(ANS, SHUF) [ ["b", "pink"], ["c", "green"], ["d", "purple"], ["e", "red"] ][INDEX] SHUF[0] SHUF[1] SHUF[2] SHUF[3] 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)

Which vector has the same `COMPONENT_NAME` component as `\vec a`?

graphInit({ range: 10, scale: 20, tickStep: 1, axisArrows: "<->", axisLabels: ['x', 'y'] }); 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}`

The `COMPONENT_NAME` component of a vector is the amount it moves DIRECTION.

style({ stroke: BLACK }); line([AOX + AX, AOY], [AOX + AX, AOY + AY], { arrows: "->" }); style({ strokeDasharray: "."}); line([AOX, AOY], [AOX + AX, AOY]);
style({ stroke: BLACK }); line([AOX, AOY + AY], [AOX + AX, AOY + AY], { arrows: "->" }); style({ strokeDasharray: "."}); line([AOX, AOY], [AOX, AOY + AY]);

Vector `\vec a` starts at `COMPONENT_NAME = [AOX, AOY][COMPONENT]` and ends at `COMPONENT_NAME = [AOX + AX, AOY + AY][COMPONENT]`.

Therefore, vector `\vec a` moves DIRECTION `[AX, AY][COMPONENT]` units.

Therefore, vector `\vec a` moves DIRECTION `1` unit.

style({ stroke: BLACK, strokeDasharray: "" }); line([ANS[2] + ANS[0], ANS[3]], [ANS[2] + ANS[0], ANS[3] + ANS[1]], { arrows: "->" }); style({ strokeDasharray: "."}); line([ANS[2], ANS[3]], [ANS[2] + ANS[0], ANS[3]]);
style({ stroke: BLACK, strokeDasharray: "" }); line([ANS[2], ANS[3] + ANS[1]], [ANS[2] + ANS[0], ANS[3] + ANS[1]], { arrows: "->" }); style({ strokeDasharray: "."}); line([ANS[2], ANS[3]], [ANS[2], ANS[3] + ANS[1]]);

The only other vector that moves DIRECTION `[AX, AY][COMPONENT]` units is `\vec ANSL`.

The only other vector that moves DIRECTION `1` unit is `\vec ANSL`.

randRangeNonZero(-8, 8) randRangeNonZero(-8, 8) randRangeNonZero(max(-9, -9 - AX), min(9, 9 - AX)) randRangeNonZero(max(-9, -9 - AY), min(9, 9 - AY)) 1 + 0.8 / sqrt(AX * AX + AY * AY) randRange(0, 1) ["x", "y"][COMPONENT] $._("horizontally") $._("vertically") [HORIZONTAL, VERTICAL][COMPONENT] [AX, AY][COMPONENT]

What is the value of the `COMPONENT_NAME` component of `\vec a`?

graphInit({ range: 10, scale: 20, tickStep: 1, labels: true, axisArrows: "<->", axisLabels: ['x', 'y'] }); style({ stroke: BLUE, color: BLUE }, function() { line([AOX, AOY], [AOX + AX, AOY + AY], { arrows: "->" }); label([AOX + AF * AX, AOY + AF * AY], "\\vec a"); });
ANS

The `COMPONENT_NAME` component of a vector is the amount it moves DIRECTION.

style({ stroke: BLACK }); line([AOX + AX, AOY], [AOX + AX, AOY + AY], { arrows: "->" }); style({ strokeDasharray: "."}); line([AOX, AOY], [AOX + AX, AOY]);
style({ stroke: BLACK }); line([AOX, AOY + AY], [AOX + AX, AOY + AY], { arrows: "->" }); style({ strokeDasharray: "."}); line([AOX, AOY], [AOX, AOY + AY]);

Vector `\vec a` starts at `COMPONENT_NAME = [AOX, AOY][COMPONENT]` and ends at `COMPONENT_NAME = [AOX + AX, AOY + AY][COMPONENT]`.

Therefore, the `COMPONENT_NAME` component of `\vec a` is `ANS`