What is motion in a plane?

Motion in a plane is motion of a particle in two dimensions, where its position, velocity, and acceleration are represented by vectors in an \(x\text{-}y\) plane.

What is a scalar quantity?

A scalar quantity is one that has only magnitude and no direction, such as mass, distance, speed, time, or temperature.

What is a vector quantity?

A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration, and force.

Define position vector in a plane.

Position vector \(\vec{r}\) of a particle at \((x,y)\) is given by \(\vec{r}=x\hat{i}+y\hat{j}\) with respect to the origin \(O(0,0)\).

Define displacement vector.

Displacement vector is the change in position: \(\Delta\vec{r}=\vec{r}_2-\vec{r}_1\), independent of the actual path followed.

Write the expressions for average velocity in a plane.

Average velocity is \(\vec{v}_{\text{avg}}=\frac{\Delta\vec{r}}{\Delta t}\), where \(\Delta\vec{r}\) is displacement in time interval \(\Delta t\).

What is instantaneous velocity in 2D?

Instantaneous velocity is \(\vec{v}=\frac{d\vec{r}}{dt}\) and is always tangent to the path at that instant.

Define average acceleration in a plane.

Average acceleration is \(\vec{a}_{\text{avg}}=\frac{\Delta\vec{v}}{\Delta t}\), where \(\Delta\vec{v}\) is change in velocity in time \(\Delta t\).

What is instantaneous acceleration in a plane?

Instantaneous acceleration is \(\vec{a}=\frac{d\vec{v}}{dt}\) and measures the rate of change of velocity vector at a given instant.

State the triangle law of vector addition.

If two vectors are represented by two sides of a triangle taken in order, the third side taken in the same order represents their resultant.

State the parallelogram law of vector addition.

If two vectors from the same point form adjacent sides of a parallelogram, the diagonal through that point gives the resultant vector.

Give formula for magnitude of resultant of two vectors.

For vectors \(\vec{A}\) and \(\vec{B}\) with angle \(\theta\) between them, resultant magnitude is \(R=\sqrt{A^2+B^2+2AB\cos\theta}\).

What is vector subtraction?

Vector subtraction \(\vec{A}-\vec{B}\) is defined as \(\vec{A}+(-\vec{B})\), where \(-\vec{B}\) has same magnitude as \(\vec{B}\) but opposite direction.

What is a unit vector?

A unit vector has magnitude 1 and gives only direction; unit vector along \(\vec{A}\) is \(\hat{A}=\frac{\vec{A}}{|\vec{A}|}\)

Give components of a vector in a plane.

If \(\vec{A}\) makes angle \(\theta\) with positive \(x\)-axis, then \(A_x=A\cos\theta\), \(A_y=A\sin\theta\), and \(\vec{A}=A_x\hat{i}+A_y\hat{j}\).

Class XI Physics · Chapter 4

Motion in a Plane

NCERT | Class 11 | Physics

The world is not a straight line. Vectors, projectiles, and circular motion — this chapter puts the curve into physics.

\(\vec{A} + \vec{B} = \vec{R}\)

📖 Start Notes ⚡ MCQs 🎯 PYQs

Motion Type

Types of Vectors

NCERT Exercises

R = u²sin2θ/g

Range Formula

JEE

Critical Chapter

Conceptual Framework

Core Topics at a Glance

➕

Scalars & Vectors

Scalars have magnitude only; vectors have magnitude and direction. Addition of vectors follows the triangle/parallelogram law, not simple arithmetic.

\(R = \sqrt{A^2+B^2+2AB\cos\theta}\)

🧭

Resolution of Vectors

Any vector can be resolved into two perpendicular components. This is the cornerstone of 2D and 3D mechanics.

\(A_x = A\cos\theta,\; A_y = A\sin\theta\)

⚙️

Dot & Cross Products

Scalar (dot) product gives a scalar: A·B = AB cosθ. Vector (cross) product gives a vector perpendicular to both: |A×B| = AB sinθ.

\(\vec{A}\cdot\vec{B} = AB\cos\theta\)

🎯

Projectile Motion

Horizontal velocity is constant; vertical motion is free fall. The trajectory is a parabola. Maximum range occurs at 45°.

\(R = u^2\sin2\theta/g\)

⭕

Uniform Circular Motion

Speed is constant but velocity changes direction continuously. Centripetal acceleration is always directed toward the centre.

\(a_c = v^2/r = \omega^2 r\)

🌊

Relative Motion in 2D

Velocity of A relative to B is vector subtraction. Key applications: river-boat problems, rain-umbrella, and aircraft navigation.

\(\vec{v}_{AB} = \vec{v}_A - \vec{v}_B\)

Quick Reference

Key Formulae

Quantity	Formula	Remarks
Resultant Magnitude	\(R = \sqrt{A^2+B^2+2AB\cos\theta}\)	Parallelogram law
Resultant Angle	\(\tan\phi = \frac{B\sin\theta}{A+B\cos\theta}\)	Angle with A
Max Height	\(H = \frac{u^2\sin^2\theta}{2g}\)	Projectile
Time of Flight	\(T = \frac{2u\sin\theta}{g}\)	Projectile
Range	\(R = \frac{u^2\sin 2\theta}{g}\)	R_max at θ=45°
Centripetal Acc.	\(a_c = \frac{v^2}{r} = \omega^2 r\)	Uniform circular motion
Angular Velocity	\(v = r\omega\)	Relation to linear speed
Period	\(T = \frac{2\pi r}{v} = \frac{2\pi}{\omega}\)	Circular motion

Study Material

All Resources for This Chapter

📖

Chapter Notes

Complete theory for Motion in a Plane — derivations, examples and NCERT pointers.

Open Notes →

⚡

MCQ Practice

50+ MCQs across difficulty levels for Motion in a Plane with full solution hints.

Start MCQs →

✔️

True / False Quiz

Sharpen conceptual clarity on Motion in a Plane — spot misconceptions instantly.

Take Quiz →

🧮

NCERT Exercises

Step-by-step solved NCERT back-exercise questions for Motion in a Plane.

View Solutions →

🎯

Previous Year Qs

Topic-wise PYQs from JEE, NEET and CBSE Boards for Motion in a Plane.

Explore PYQs →

Exam-Ready Insights

Important Points to Remember

Triangle law: if two vectors are represented by two sides of a triangle, the resultant is the closing side (head to tail).

At maximum height in projectile, vertical velocity = 0 but horizontal velocity = u cosθ (unchanged).

Range is same for complementary angles (θ and 90°−θ). Range is maximum at θ = 45°.

Centripetal force is not a new type of force — it is the net force directed toward the centre provided by existing forces (tension, gravity, normal).

A×B = −B×A — cross product is anti-commutative. A·B = B·A — dot product is commutative.

In river-boat problems, to cross in minimum time, boat must be directed perpendicular to the river (not considering drift).

Competitive Exams

Exam Corner

Motion in a Plane is tested across all major competitive examinations. Here are the most frequently tested topics:

⚡ JEE Main🔷 JEE Advanced🟢 NEET🟡 CBSE Board

AllProjectile motion — range, height, time

JEEVector addition and components — numerical

NEETCentripetal acceleration and force

JEERelative velocity in 2D — river-boat

BoardDerivation of range & max height

JEEDot and cross product — applications

AllUniform circular motion — conceptual

Ready to Test Yourself?

Jump into the MCQ bank or the True–False quiz to gauge how well you've understood Motion in a Plane.

⚡ MCQ Practice ✔️ True–False Quiz 🎯 PYQ Bank

← Previous ChapterMotion in a Straight LineChapter 2 Next Chapter →Laws of MotionChapter 4

📚

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

Sharing this chapter

NCERT Class 11 Physics: Motion in a Plane – Complete Notes, Formulas, PYQs & MCQs

NCERT Class 11 Physics: Motion in a Plane – Complete Notes, Formulas, PYQs & MCQs — Complete Notes & Solutions · academia-aeternum.com

Motion in a plane marks a decisive step forward in the study of mechanics, as it extends the ideas of motion from a straight line to two dimensions. In this chapter, students move beyond simple one-dimensional descriptions and begin to understand how real motion occurs in space, where both magnitude and direction play equally important roles. The concepts introduced here—such as vectors, their resolution, and vector addition—form the mathematical and conceptual backbone of two-dimensional…

🎓 Class 11 📐 Physics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE

Share on