Is Plane part of the EAPCET Mathematics syllabus?

Yes. Plane is taught in Intermediate first year · Paper IB 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 Plane?

Dividing by a² + b² + c² instead of its square root in the distance formula. Finding the distance between parallel planes like 2x + y − 2z = 3 and 4x + 2y − 4z = 1 without first making the x, y, z coefficients identical. Reading intercepts from 2x + 3y + 6z = 12 as 2, 3, 6; divide by 12 first to get x/6 + y/4 + z/2 = 1, so the intercepts are 6, 4 and 2. Using the angle between normals for the angle between a line and a plane; that angle uses sin θ, not cos θ.

EAPCET Mathematics · Intermediate first year · Paper IB

Plane

The Plane chapter covers the equation of a plane in its standard forms, the angle between planes and the distance of a point from a plane.

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

Key formulas and results

$ax + by + cz + d = 0$ has normal direction ratios $(a, b, c)$
Intercept form: $\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1$
Normal form: $lx + my + nz = p$
Distance of $(x_{1}, y_{1}, z_{1})$ from the plane $= \dfrac{|ax_{1} + by_{1} + cz_{1} + d|}{\sqrt{a^{2} + b^{2} + c^{2}}}$
Angle between planes: $\cos\theta = \dfrac{|a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2}|}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}}\,\sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$

What this chapter covers

General, intercept and normal forms of a plane
Angle between two planes
Distance of a point from a plane

How it is usually asked

Find the equation of a plane
Find the angle between two planes
Find a distance or intercepts

Understanding Plane

A plane is fixed by a point on it and a normal vector perpendicular to it. If the normal has direction ratios (a, b, c), the plane is ax + by + cz + d = 0, and conversely the coefficients of x, y and z in any plane’s equation give its normal directly. A plane through (x₁, y₁, z₁) with that normal is a(x − x₁) + b(y − y₁) + c(z − z₁) = 0.

The same plane can be written in other forms. The intercept form x/a + y/b + z/c = 1 shows where it cuts the axes. The normal form lx + my + nz = p uses the unit normal (l, m, n) and the distance p ≥ 0 of the plane from the origin, and is obtained by dividing the general form by √(a² + b² + c²).

Angles and distances all come from the normal. The angle between two planes is the angle between their normals, the distance of a point from ax + by + cz + d = 0 is |ax₁ + by₁ + cz₁ + d|/√(a² + b² + c²), and parallel planes have proportional normals. EAPCET asks for plane equations, intercepts, angles between planes and distances.

Worked example

EAPCET-style question

The perpendicular distance of the point $(1, -2, 3)$ from the plane $2x - y + 2z + 4 = 0$ is

(1) $\dfrac{14}{3}$
(2) $\dfrac{10}{3}$
(3) $\dfrac{14}{9}$
(4) $\dfrac{4}{3}$

Solution

Substitute the point: $2(1) - (-2) + 2(3) + 4 = 2 + 2 + 6 + 4 = 14$ .
$\sqrt{2^{2} + (-1)^{2} + 2^{2}} = \sqrt{9} = 3$ .
Distance $= \dfrac{|14|}{3} = \dfrac{14}{3}$ .

Answer: $\dfrac{14}{3}$

Common mistakes to avoid

Dividing by a² + b² + c² instead of its square root in the distance formula.
Finding the distance between parallel planes like 2x + y − 2z = 3 and 4x + 2y − 4z = 1 without first making the x, y, z coefficients identical.
Reading intercepts from 2x + 3y + 6z = 12 as 2, 3, 6; divide by 12 first to get x/6 + y/4 + z/2 = 1, so the intercepts are 6, 4 and 2.
Using the angle between normals for the angle between a line and a plane; that angle uses sin θ, not cos θ.

How to prepare it

Everything in this chapter flows from the normal vector (a, b, c) — identify it first.

Once the formulas feel familiar, test them the way the exam does: practise Plane 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 Plane 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 Plane part of the EAPCET Mathematics syllabus?: Yes. Plane is taught in Intermediate first year · Paper IB 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 Plane for EAPCET?: Everything in this chapter flows from the normal vector (a, b, c) — identify it first.
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 Plane?: Dividing by a² + b² + c² instead of its square root in the distance formula. Finding the distance between parallel planes like 2x + y − 2z = 3 and 4x + 2y − 4z = 1 without first making the x, y, z coefficients identical. Reading intercepts from 2x + 3y + 6z = 12 as 2, 3, 6; divide by 12 first to get x/6 + y/4 + z/2 = 1, so the intercepts are 6, 4 and 2. Using the angle between normals for the angle between a line and a plane; that angle uses sin θ, not cos θ.