Class 12 Vectors and 3D Geometry Important Questions | CBSE Maths 2026

Class 12 Vectors and 3D Geometry Important Questions (CBSE) – Easy Guide to Pass Exam

Vectors and Three-Dimensional Geometry are among the highest-scoring chapters in CBSE Class 12 Mathematics. Together, these chapters usually carry 10–14 marks, and questions are often direct, formula-based, and repeated in pattern every year.

If practiced properly, Vectors and 3D Geometry can guarantee full marks even for average students.

This article explains important questions, concepts, formulas, and exam focus areas in a very easy and clear manner.

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Why Vectors and 3D Geometry Are Important for Class 12 CBSE?

• Questions are predictable and formula-based

• Diagrams are simple and scoring

• Step-wise marking helps students score even with partial answers

• Perfect chapters for last-minute revision

Board Tip: Neat presentation + correct formula = easy marks.

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Weightage of Vectors & 3D Geometry (CBSE Exam)

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Important Topics from Vectors (Class 12)

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Most Important Vectors Questions for Board Exam

1. Find the Magnitude of a Vector

Question Type: Very Short / Short Answer

If

a⃗=3i^+4j^−12k^\vec{a} = 3\hat{i} + 4\hat{j} - 12\hat{k}a=3i^+4j^​−12k^

Magnitude:

∣a⃗∣=32+42+(−12)2|\vec{a}| = \sqrt{3^2 + 4^2 + (-12)^2}∣a∣=32+42+(−12)2​

Frequently asked

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2. Find Angle Between Two Vectors

Formula:

a⃗⋅b⃗=∣a⃗∣∣b⃗∣cos⁡θ\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\thetaa⋅b=∣a∣∣b∣cosθ

✔ Always write formula
✔ Substitute values clearly
✔ Final answer in degrees

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3. Prove Vectors Are Perpendicular

Condition:

a⃗⋅b⃗=0\vec{a} \cdot \vec{b} = 0a⋅b=0

Very common prove-type question

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4. Find Vector Equation of a Line

r⃗=a⃗+λb⃗\vec{r} = \vec{a} + \lambda \vec{b}r=a+λb

Where:

• a = position vector

• b = direction vector

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Important Topics from 3D Geometry

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Most Important 3D Geometry Questions

1. Find Direction Cosines

If direction ratios are a, b, c

l=aa2+b2+c2,  m=ba2+b2+c2,  n=ca2+b2+c2l = \frac{a}{\sqrt{a^2+b^2+c^2}},\; m = \frac{b}{\sqrt{a^2+b^2+c^2}},\; n = \frac{c}{\sqrt{a^2+b^2+c^2}}l=a2+b2+c2​a​,m=a2+b2+c2​b​,n=a2+b2+c2​c​

Very high probability question

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2. Equation of a Line in 3D

Using point and direction ratios

x−x1a=y−y1b=z−z1c\frac{x-x_1}{a} = \frac{y-y_1}{b} = \frac{z-z_1}{c}ax−x1​​=by−y1​​=cz−z1​​

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3. Equation of a Plane

General form:

$$ax+by+cz+d=0$$

Plane through point:

a(x−x1)+b(y−y1)+c(z−z1)=0a(x-x_1) + b(y-y_1) + c(z-z_1) = 0a(x−x1​)+b(y−y1​)+c(z−z1​)=0

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4. Distance of a Point from a Plane

Distance=∣ax1+by1+cz1+d∣a2+b2+c2\text{Distance} = \frac{|ax_1 + by_1 + cz_1 + d|} {\sqrt{a^2 + b^2 + c^2}}Distance=a2+b2+c2​∣ax1​+by1​+cz1​+d∣​

Asked almost every year

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Most Repeated Board-Level Questions (Quick Table)

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How to Score Full Marks in Vectors & 3D Geometry

✔ Write formulas clearly
✔ Draw neat diagrams
✔ Don’t skip steps
✔ Use correct symbols
✔ Final answer should be boxed

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Last-Minute Revision Strategy (1 Day Plan)