Is Addition of Vectors part of the EAPCET Mathematics syllabus?

Yes. Addition of Vectors is taught in Intermediate first year · Paper IA Mathematics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.

How many Mathematics questions are there in EAPCET?

80 of the 160 questions in the Engineering paper are Mathematics, spread across 37 chapters.

What mistakes do students make in Addition of Vectors?

Attaching m to a⃗ in the section formula; for the ratio m : n from A to B, m multiplies b⃗, the far end. Writing AB⃗ = a⃗ − b⃗; the vector from A to B is b⃗ − a⃗ (head minus tail). Giving a⃗ itself when a unit vector is asked; divide by |a⃗| first. Testing coplanarity of three points instead of four; any three points are always coplanar, so the test needs four points or three vectors.

EAPCET Mathematics · Intermediate first year · Paper IA

Addition of Vectors

Addition of Vectors introduces vectors as quantities with direction, position vectors, the section formula and the vector equations of lines and planes.

Subject: Mathematics
Taught in: Intermediate first year · Paper IA
Mathematics in the paper: 80 of 160 questions

Key formulas and results

Point dividing $AB$ internally in the ratio $m : n$ has position vector $\dfrac{m\vec{b} + n\vec{a}}{m + n}$ .
Centroid of a triangle with vertices $\vec{a}, \vec{b}, \vec{c}$ is $\dfrac{\vec{a} + \vec{b} + \vec{c}}{3}$ .
Unit vector along $\vec{a}$ is $\dfrac{\vec{a}}{|\vec{a}|}$ .
Line through $\vec{a}$ parallel to $\vec{b}$ : $\vec{r} = \vec{a} + t\vec{b}$ .
Points $A, B, C$ are collinear when $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are parallel.
$\vec{a} = a_{1}\hat{i} + a_{2}\hat{j} + a_{3}\hat{k}$ and $\vec{b} = b_{1}\hat{i} + b_{2}\hat{j} + b_{3}\hat{k}$ are collinear $(\vec{a} = \lambda\vec{b})$ iff $\dfrac{a_{1}}{b_{1}} = \dfrac{a_{2}}{b_{2}} = \dfrac{a_{3}}{b_{3}}$
Points of trisection of $AB$ : $\dfrac{2\vec{a} + \vec{b}}{3}$ and $\dfrac{\vec{a} + 2\vec{b}}{3}$
$\overrightarrow{PQ}$ = (position vector of $Q$ ) − (position vector of $P$ )

What this chapter covers

Classification of vectors and vector addition
Position vectors and the section formula
Linear combinations, collinearity and coplanarity
Vector equation of a line and of a plane

How it is usually asked

Test whether points are collinear or vectors coplanar
Find the point that divides a segment in a given ratio
Write the vector equation of a line or plane

Understanding Addition of Vectors

A vector has both magnitude and direction, and two vectors are equal when both match, wherever they are drawn. Vectors are added by the triangle law: place the tail of the second at the head of the first, and the sum runs from the start to the end. In components, a⃗ = a₁i + a₂j + a₃k, so addition and scalar multiplication are done coordinate by coordinate, and |a⃗| = √(a₁² + a₂² + a₃²).

Fixing an origin O lets every point be described by its position vector. Then AB⃗ = b⃗ − a⃗, the point dividing AB internally in the ratio m : n has position vector (m b⃗ + n a⃗)/(m + n), and the centroid of a triangle is the average of its vertices. Three points are collinear when one of AB⃗, AC⃗ is a scalar multiple of the other.

The same ideas give the vector equation of a line, r⃗ = a⃗ + t b⃗, which is a fixed point plus any multiple of a direction, and of a plane through a point spanned by two directions. EAPCET questions ask for section points, unit vectors, collinearity or coplanarity tests and these equations, and all of them reduce to careful component arithmetic.

Worked example

EAPCET-style question

$A$ and $B$ have position vectors $2\hat{i} + 3\hat{j} - \hat{k}$ and $5\hat{i} - 3\hat{j} + 2\hat{k}$ . The position vector of the point dividing $AB$ internally in the ratio $1 : 2$ is

(1) $3\hat{i} + \hat{j}$
(2) $4\hat{i} - \hat{j} + \hat{k}$
(3) $\dfrac{7\hat{i} + \hat{k}}{2}$
(4) $3\hat{i} - \hat{j}$

Solution

With $m : n = 1 : 2$ , the point is $\dfrac{1 \cdot \vec{b} + 2 \cdot \vec{a}}{3}$ .
$1 \cdot \vec{b} + 2 \cdot \vec{a} = (5 + 4)\hat{i} + (-3 + 6)\hat{j} + (2 - 2)\hat{k} = 9\hat{i} + 3\hat{j}$ .
Divide by 3 to get $3\hat{i} + \hat{j}$ .
The option $4\hat{i} - \hat{j} + \hat{k}$ comes from swapping the ratio, and $\tfrac{7\hat{i} + \hat{k}}{2}$ is the midpoint.

Answer: $3\hat{i} + \hat{j}$

Common mistakes to avoid

Attaching m to a⃗ in the section formula; for the ratio m : n from A to B, m multiplies b⃗, the far end.
Writing AB⃗ = a⃗ − b⃗; the vector from A to B is b⃗ − a⃗ (head minus tail).
Giving a⃗ itself when a unit vector is asked; divide by |a⃗| first.
Testing coplanarity of three points instead of four; any three points are always coplanar, so the test needs four points or three vectors.

How to prepare it

Translate geometry into position vectors early; most problems then become algebra.

This chapter is the foundation for Product of Vectors — keep the notation consistent between the two.

Once the formulas feel familiar, test them the way the exam does: practise Addition of Vectors questions chapter-wise, then attempt a full previous year paper to see whether it holds up under a 3-hour timer.

Related Mathematics chapters

See every chapter in the EAPCET Mathematics syllabus.

Practise Addition of Vectors chapter-wise

Chapter-wise quizzes show exactly which topics in this chapter you still get wrong — before a full paper does.

Frequently asked questions

Is Addition of Vectors part of the EAPCET Mathematics syllabus?: Yes. Addition of Vectors is taught in Intermediate first year · Paper IA Mathematics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.
How should I prepare Addition of Vectors for EAPCET?: Translate geometry into position vectors early; most problems then become algebra. This chapter is the foundation for Product of Vectors — keep the notation consistent between the two.
How many Mathematics questions are there in EAPCET?: 80 of the 160 questions in the Engineering paper are Mathematics, spread across 37 chapters.
What mistakes do students make in Addition of Vectors?: Attaching m to a⃗ in the section formula; for the ratio m : n from A to B, m multiplies b⃗, the far end. Writing AB⃗ = a⃗ − b⃗; the vector from A to B is b⃗ − a⃗ (head minus tail). Giving a⃗ itself when a unit vector is asked; divide by |a⃗| first. Testing coplanarity of three points instead of four; any three points are always coplanar, so the test needs four points or three vectors.