back":"To find the vector $\\vec{AB}$, use the rule $\\boxed{\\vec{OB} - \\vec{OA}}$, often remembered as end minus start.","points":null},{"id":"e3316fb7-9a04-4c57-a152-25d0a791ec3f","cardType":"cloze","front":"To find the vector $\\vec{AB}$, use the rule $\\vec{OB} - \\vec{OA}$, often remembered as [ ].","back":"To find the vector $\\vec{AB}$, use the rule $\\vec{OB} - \\vec{OA}$, often remembered as end minus start.","points":null},{"id":"f04f7475-0497-4174-9045-e661cf5ce0bb","cardType":"basic","front":"If point $P$ divides the line $AB$ in the ratio $m:n$, what fraction of $\\vec{AB}$ is the vector $\\vec{AP}$?","back":"$$\\frac{m}{m+n}$","points":1},{"id":"d9b27543-eaaf-4735-a560-197b6714f377","cardType":"cloze","front":"If $AP:PB = 2:3$, then point $P$ is $\\text{[...]}$ of the way from $A$ to $B$.","back":"If $AP:PB = 2:3$, then point $P$ is $\\boxed{\\frac{2}{5}}$ of the way from $A$ to $B$.","points":null},{"id":"3efceab0-2c45-4e59-a5b7-5414b4ead33b","cardType":"basic","front":"How do you calculate the position vector $\\vec{OP}$ for a point $P$ on the line $AB$?","back":"$$\\vec{OP} = \\vec{OA} + \\text{fraction} \\times \\vec{AB}$","points":1},{"id":"b60634c8-b502-497b-8b26-8b8888575741","cardType":"basic","front":"What two conditions prove that points $A, B$ and $C$ are collinear?","back":"

The vectors (e.g., $\\vec{AB}$ and $\\vec{AC}$) are scalar multiples.
The vectors share a common point.

","points":2},{"id":"2b58682a-1fb2-4aef-8b0c-aa811d93be84","cardType":"cloze","front":"If $\\vec{AD} = \\lambda\\vec{AE}$, the vectors are [ ] and, because they share point $A$, the points are collinear.","back":"If $\\vec{AD} = \\lambda\\vec{AE}$, the vectors are parallel and, because they share point $A$, the points are collinear.","points":null},{"id":"48d1c834-f8ba-4d7d-98ef-21ca5f02bd1a","cardType":"cloze","front":"If $\\vec{AD} = \\lambda\\vec{AE}$, the vectors are parallel and, because they share point $A$, the points are [ ].","back":"If $\\vec{AD} = \\lambda\\vec{AE}$, the vectors are parallel and, because they share point $A$, the points are collinear.","points":null},{"id":"23f5abbf-ef4b-461d-8638-674c91b1fa72","cardType":"basic","front":"Why is showing $\\vec{OD} = \\lambda\\vec{OE}$ insufficient to prove points $A, D, E$ are collinear?","back":"It only proves $O, D, E$ are on a line; it does not link them to point $A$.","points":2},{"id":"d4cd4cf9-207d-4ca7-9064-65f18f48da75","cardType":"basic","front":"In a parallelogram $OABC$ where $\\vec{OA}=a$ and $\\vec{OC}=c$, what is the position vector of the diagonal vertex $B$?","back":"$$\\vec{OB} = a + c$","points":1},{"id":"cf1fb6eb-875e-4a44-be16-ffbae2de0c23","cardType":"cloze","front":"In a regular hexagon with centre $O$, if $\\vec{OP}=p$ and $\\vec{OQ}=q$, the next vertex $R$ has position vector $\\vec{OR} = $ $\\text{[...]}$.","back":"In a regular hexagon with centre $O$, if $\\vec{OP}=p$ and $\\vec{OQ}=q$, the next vertex $R$ has position vector $\\vec{OR} = $ $\\boxed{q - p}$.","points":null},{"id":"b818a7c0-c76c-4df7-b541-d3f6fa320bcc","cardType":"basic","front":"In a regular hexagon with centre $O$, if $\\vec{OQ}=q$, what is the position vector of the opposite vertex $T$?","back":"$$-q$","points":1},{"id":"1dbe0754-9d64-4111-bbb5-b1a28d5bbc97","cardType":"basic","front":"If $Y$ lies on $PQ$ extended beyond $Q$ such that $PQ:QY = 3:2$, express $\\vec{QY}$ in terms of $\\vec{PQ}$.","back":"$$\\vec{QY} = \\frac{2}{3}\\vec{PQ}$","points":1},{"id":"431171b5-5736-4879-b5a3-393554efcace","cardType":"cloze","front":"To find an unknown vector on an extension (e.g., $E$ on $OB$), introduce an unknown scalar $x$ such that $\\vec{BE

Vectors Proof Questions Flashcards

Vectors Proof Questions Flashcards

Vectors Proof Questions Flashcards

Vectors Proof Questions Flashcards