:[{"id":"107a09a5-52d2-4c28-b401-e3015fc5d6d3","label":"0","content":"Given that $|3\\mathbf{i} + k\\mathbf{j}| = 3\\sqrt{17}$\n\nFind the value of $k$","markscheme":"$$$\\sqrt{3^2 + k^2} = 3\\sqrt{17}$$\n$$3^2 + k^2 = (3\\sqrt{17})^2$$\n$$9 + k^2 = 153$$\n$$k^2 = 144$$\n$$k = \\pm 12$$ M1 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Sets up equation $3^2 + k^2 = (3\\sqrt{17})^2$.","code":"M"},{"id":"p2","marks":1,"description":"Finds $k = \\pm 12$.","code":"A"}],"finalAnswers":["12","-12"],"generatedAt":"2026-05-12T02:14:06.603Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"12e841aa-54a1-4f78-9229-64fa19db4936","revisionId":"c3a1f736-b739-4a83-9670-0a02db5cfa76","questionNumber":"3","questionType":"LA","specification":"Given that the point $A$ has position vector $-5\\mathbf{i} + 7\\mathbf{j}$ and the point $B$ has position vector $-8\\mathbf{i} + 2\\mathbf{j}$","difficulty":1,"totalMarks":4,"sourceTitle":"Question Set 11: Vectors","parts":[{"id":"c82c835c-c340-4ffb-89d6-1bb0d6a3fa72","label":"a","content":"Find the vector $\\vec{AB}$","markscheme":"$$$\\begin{pmatrix} -8 \\\\ 2 \\end{pmatrix} - \\begin{pmatrix} -5 \\\\ 7 \\end{pmatrix} = \\begin{pmatrix} -3 \\\\ -5 \\end{pmatrix}$$\n\nFinal answer: $-3\\mathbf{i} - 5\\mathbf{j}$ M1 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Subtracts position vector $A$ from position vector $B$.","code":"M"},{"id":"p2","marks":1,"description":"Correct vector $-3\\mathbf{i} - 5\\mathbf{j}$.","code":"A"}],"finalAnswers":["-3i - 5j"],"generatedAt":"2026-05-12T02:14:06.603Z","modelVersion":"gemini-3-flash-preview"}},{"id":"318e2eca-0d55-44a8-bafb-990166331bd3","label":"b","content":"Find $|\\vec{AB}|$","markscheme":"$$$\\sqrt{3^2 + 5^2} = \\sqrt{34}$$ M1 A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Uses Pythagoras' theorem on their vector components.","code":"M"},{"id":"p2","marks":1,"description":"Final answer $\\sqrt{34}$.","code":"A"}],"finalAnswers":["\\sqrt{34}"],"generatedAt":"2026-05-12T02:14:06.603Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"ca48e482-22c2-4abc-874f-83d0949750ac","revisionId":"28483adf-92e2-4d0e-9eb3-47bec28951c0","questionNumber":"4","questionType":"LA","specification":"$$\\mathbf{a} = -5\\mathbf{i} + 7\\mathbf{j}$ and $\\mathbf{b} = x\\mathbf{i} + y\\mathbf{j}$","difficulty":1,"totalMarks":2,"sourceTitle":"Question Set 11: Vectors","parts":[{"id":"d1e51acd-f28e-45ab-8bb3-613e09160b53","label":"0","content":"Given that the resultant force of $\\mathbf{a}$ and $\\mathbf{b}$ is $-2\\mathbf{i} - 3\\mathbf{j}$ find the values of $x$ and $y$","markscheme":"$$$\\begin{pmatrix} -5 \\\\ 7 \\end{pmatrix} + \\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} -2 \\\\ -3 \\end{pmatrix}$$\n\n$x = 3$\n$y = -10$ M1 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Sets up vector addition equation.","code":"M"},{"id":"p2","marks":1,"description":"Finds $x = 3$ and $y = -10$.","code":"A"}],"finalAnswers":["x=3, y=-10"],"generatedAt":"2026-05-12T02:14:06.603Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"3280967f-9338-4c8c-ba03-9faed53b5482","revisionId":"a0e50cf4-edff-4d01-8cfc-ad71d4be2b89","questionNumber":"5","questionType":"LA","specification":"In triangle $ABC$, $\\vec{AB} = 6\\mathbf{i} + 2\\mathbf{j}$, $\\vec{AC} = 8\\mathbf{i} - 5\\mathbf{j}$","difficulty":1,"totalMarks":4,"sourceTitle":"Question Set 11: Vectors","parts":[{"id":"0bc4c339-0b8b-4b55-92ca-350da8ee8fbe","label":"a","content":"Find the vector $\\vec{BC}$","markscheme":"$$$\\vec{BC} = \\vec{BA} + \\vec{AC}$$\n$$= \\begin{pmatrix} -6 \\\\ -2 \\end{pmatrix} + \\begin{pmatrix} 8 \\\\ -5 \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ -7 \\end{pmatrix}$$\n\nFinal answer: $2\\mathbf{i} - 7\\mathbf{j}$ M1 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"poi