Vector components, products and spatial geometry topic check
Practise vector components, products and spatial geometry, check independently, and return later to review. This check covers selected skills, not the whole course topic.
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Learning goals
- Add vectors by ordered components
- Subtract vectors by ordered components
- Multiply a vector by a scalar
- Calculate the magnitude of a vector
- Produce a unit vector in a given direction
- Locate a point from a displacement parameter
- Find the directed displacement between two points
- Calculate the distance between two points
- Test all coordinates for point collinearity
- Locate an internally or externally dividing point from its ratio
- Calculate a scalar product
- Calculate an ordered vector product
- Calculate the angle between directed vectors
- Find a signed scalar component along a direction
- Find the parallel vector component along a direction
- Find the perpendicular component's magnitude
- Produce a vector equation of a spatial line
- Produce independent Cartesian equalities for a spatial line
- Produce a vector equation of a plane
- Produce a Cartesian equation of a plane
- Distinguish coincident, parallel, intersecting and skew lines
- Classify a line's relationship with a plane
- Distinguish coincident, parallel and intersecting planes
- Produce the intersection line of two planes
- Find the foot of a perpendicular from a point to a line
- Find the perpendicular distance from a point to a line
- Find the foot of a perpendicular from a point to a plane
- Find the perpendicular distance from a point to a plane
- Find the unique intersection point of a line and a plane
- Find the smaller angle between spatial lines
- Find the smaller angle between planes
- Find the angle between a line and a plane
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Check what you know
Answer each question and say how sure you are to find what to practise next.
Check what you know
Start here to see which parts you already know.
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Paper instructions
This shows what to work on next and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
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Recent attempts
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No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Starting check complete
Next steps
Where marks were lost
Your answers
Practise
Practise questions on the skills you are learning.
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Use the feedback to improve your answers; this practice does not count towards your progress.
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Paper instructions
This is for practice only and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you check each answer.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Practise after feedback
After a check, practise the skills it showed you need to work on.
Questions are unavailable
Checking question availability…
Use the feedback to improve your answers; this practice does not count towards your progress.
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
This is for practice only and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you check each answer.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Check your progress
When you feel ready, answer on your own to show what you can do.
Questions are unavailable
Checking question availability…
Use the feedback to improve your answers; this practice does not count towards your progress.
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
Your result can count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Progress check complete
Next steps
Where marks were lost
Your answers
Check again
After practising what your progress check showed, check those skills again.
Questions are unavailable
Checking question availability…
Use the feedback to improve your answers; this practice does not count towards your progress.
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
Your result can count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Progress check complete
Next steps
Where marks were lost
Your answers
Retention check
Come back later to see whether your learning has lasted.
Questions are unavailable
Checking question availability…
Use the feedback to improve your answers; this practice does not count towards your progress.
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
A scheduled review counts towards your course progress only when it is due.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Retention check complete
Next steps
Where marks were lost
Your answers
Next step