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 \(\vec{A}=A_x\hat{i}+A_y\hat{j}\).

NCERT Class XI · Physics · Chapter 3

Motion in a Plane True–False Lab

Use this dedicated True–False set to stress‑test your understanding of vectors, projectile motion, relative velocity and uniform circular motion before attempting full‑length numericals or JEE/NEET‑level questions.

Scalars vs Vectors Dot & Cross Products Projectile Motion Formulae Uniform Circular Motion Relative Motion & River–Boat

Start the True–False Challenge 25 conceptual statements covering vectors, parabolic trajectories, UCM and relative velocity – mark T/F then justify each in one line.

Concept
Integrity
Check

Vectors & Components

Projectile Motion

Circular Motion

Chapter Snapshot

Motion in a Plane brings 1D kinematics into two dimensions using vectors, and underpins projectile motion, relative motion and uniform circular motion.

Why True–False?

Targets the most common misconceptions in vectors, projectiles, UCM and relative velocity.
Prepares you for statement‑based “correct/incorrect” MCQs in Boards and JEE/NEET.
Forces you to think in terms of components, directions and limiting cases, not just formulas.

Best Use

Warm‑up before a practice sheet or test on Motion in a Plane.
End‑of‑day revision: pick 5–10 statements and write reason in one line.
Group discussion: defend your answer using diagrams or equations.

Scalars, Vectors & Components

Distinguish scalar vs vector quantities, test when vectors are equal, and practise resolving any vector into unique components along chosen perpendicular axes. Many statements here probe sign conventions and “perpendicular / parallel” logic via dot and cross products.

Dot & Cross Products

Use \(\vec{A}\cdot\vec{B}=AB\cos\theta\) to detect perpendicularity and projections, and \(|\vec{A}\times\vec{B}|=AB\sin\theta\) plus the right‑hand rule for area and direction. Several True–False items hinge on recognising when these products vanish or become maximum.

Projectile Motion & Parabolic Path

Horizontal velocity component stays constant; vertical component changes uniformly under gravity, giving a parabolic trajectory on level ground. Statements about time of flight, range, complementary angles and “same height” speeds are designed to check your grasp of these standard results.

Uniform Circular Motion

In UCM, speed is constant but velocity and acceleration directions keep changing; acceleration is \(v^{2}/r\) toward the centre and tangential acceleration is zero. Some statements test how centripetal acceleration scales when speed or radius are changed.

Relative Velocity & River–Boat

Relative velocity \(\vec{v}_{BA} = \vec{v}_B - \vec{v}_A\) governs rain‑man and river‑boat problems. The True–False questions here ensure you can reason about shortest time vs shortest path and interpret “velocity of A with respect to B” correctly.

How to Use This True–False Set for Maximum Gain

1. Do not guess: for every statement, decide T/F and immediately quote a formula, vector diagram or limiting case that supports your choice.
2. Pay attention to words like “always”, “only”, “remains unchanged” – most false statements break precisely because of these extremes.
3. When stuck, quickly split motion into x and y components or tangential and radial components; this resolves half of the conceptual confusion in 2D motion.
4. After finishing, mark the statements you got wrong and revisit the corresponding theory sections (vectors, projectile, UCM, relative motion) in your notes.

Ready? Scroll down to the True–False questions list below and start with: “A physical quantity that has only magnitude and no direction is called a scalar” and continue through projectiles, circular motion and relative velocity. Treat each as a mini concept‑check before you move to numericals.

MOTION IN A PLANE — Learning Resources

📝 Exercises

MOTION IN A PLANE-Exercise

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