Mathematics / Topic coverage

Vectors & 3D

Be fluent in planes, lines, feet of perpendiculars, and vector triple products under MC/NUM.

Weight mediumIntensity Core · weeklyTrend Rising300-target 10.8 /100medium

Path to 300

Mark budget for this portion

At ~11.2% of math weight, this portion should reliably deliver ~11 of your 100 math marks — treat misses here as rank-droppers.

8.1Floor marks

10.8Target marks

12.5Stretch marks

11.2%Of subject weight

100Subject target

At a glance

Coverage metrics

27Tagged questions

11.2%Of Mathematics

3.86Average / year

2023Peak year (7 Q)

7/7Years present

Official · 2026

Syllabus map for this portion

Full Mathematics syllabus →

Maps to Vectors unit + Analytical Geometry three-dimensional portion.

Must cover from syllabus

Dot/cross/triple product geometry
Skew lines & shortest distance
Plane equation; distance; line–plane angle

Gaps / exclusions to watch

Coplanarity checks under time pressure

Unit 01

Vectors

medium

Exam focusDot/cross/triple products with geometric meaning; orthogonal systems.

Syllabus points

Addition of vectors; scalar multiplication
Dot and cross products
Scalar and vector triple products and geometrical interpretations

Do / check

Keep geometric meaning (area/volume/coplanarity) beside algebra

Unit 02

Analytical Geometry (Three dimensions)

medium

Exam focusPlanes, skew lines, shortest distance, line–plane angles.

Syllabus points

Distance between two points; direction cosines and ratios
Equation of a straight line in space; skew lines; shortest distance
Equation of a plane; distance of a point from a plane
Angles: line–line, plane–plane, line–plane; coplanar lines

Do / check

Sketch normals before computing angles
Verify a known point lies on the plane

2020–2026

Year-wise appearance

Counts of tagged questions for this topic each year.

203

211

223

237

244

255

264

Reading the pattern

Vectors & 3D accounts for ~11.2% of tagged math questions (2020–2026).
Trend signal: rising (early-window avg 2.3/yr vs recent avg 4.3/yr).
Appears in 7/7 tagged years; peak 2023 (7 Q), low 2021 (1 Q).
Dominant subtopics: 3D Geometry (15), Vectors (12).
Question-type mix: Multi correct 44.4%, Numerical 25.9%, Matching 18.5%, Single correct 11.1%.

Internal breakdown

Subtopic coverage

Start with the top subtopics — they usually carry most of this portion’s weight.

3D Geometry15 · 55.6%
Vectors12 · 44.4%

Subtopic	Count	Share	Years (count)
3D Geometry	15	55.6%	2020·2 2022·1 2023·5 2024·3 2025·2 2026·2
Vectors	12	44.4%	2020·1 2021·1 2022·2 2023·2 2024·1 2025·3 2026·2

Exam form

Type & difficulty mix

Question types

Multi correct — 12 questions (44.4%)
Numerical — 7 questions (25.9%)
Matching — 5 questions (18.5%)
Single correct — 3 questions (11.1%)

Difficulty (heuristic)

H — 19 questions
M — 8 questions

Use for planning load only — not an official difficulty label.

Focused study

Plan for this portion

Must know

Plane from two directions + point
Shortest distance line–line / point–plane
Orthogonality of matrices / columns
Scalar & vector triple product identities

Common traps

Normal vector cross product order errors
Forgetting absolute value in distances

Weekly drill checklist

2 plane/line numericals
1 vector identity MC
1 3D matching/linked

Prerequisite chain

Vector algebra→lines→planes→shortest distance→applications

Often joins with

Algebra (matrices)Coordinate Geometry

Paper pointers

Sample tagged questions

Use these as deliberate practice targets from past papers.

Year	Paper	Q	Subtopic	Type	Diff
2020	P1	Q11	3D Geometry	MC	H
2020	P2	Q10	3D Geometry	MC	H
2020	P2	Q11	Vectors	MC	H
2021	P1	Q19	Vectors	NUM	M
2022	P1	Q12	Vectors	MC	H
2022	P1	Q16	3D Geometry	MATCH	H

Mathematics

Other portions

Algebra Calculus Coordinate Geometry Trigonometry

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