NEB Class 11 • Physics • Worked Practice

Vectors Practice Set: NEB 11 Physics

Build accuracy from vector language to components, resultants and products through a graded practice set with complete reasoning—not answer-only shortcuts.

Three levels: foundation, method and transfer
Ten fully worked problems plus a timed self-test
Every solution includes a sign, direction or magnitude check

Practice boundary

What this Vectors practice set measures

This set assesses meaning, arrow notation, rectangular components, vector addition and subtraction, magnitude and direction, and introductory scalar and vector products. Review the detailed Vectors concept guide or the Vectors study guide when a method is unfamiliar. The current CDC Physics Grade 11 page is the Nepal scope checkpoint.

The component method used here follows the coordinate-system and vector-algebra approach explained by OpenStax vector components and OpenStax vector algebra. International references deepen the physics but do not replace current Nepal course instructions.

Evidence	Credit for yourself	Warning sign
Diagram and axes	Directions and reference angle are labelled	Signs appear only after calculator work
Method	Component or graphical rule is stated	Magnitudes are added without direction
Result	Magnitude, unit and unambiguous direction	An angle is reported without its reference
Check	Quadrant, range or reverse operation	The same arithmetic is merely repeated

Five-minute start

Diagnostic: can you set up a vector problem?

Without a calculator, state the component signs for each direction: north of east, south of east, north of west and south of west. Then explain why the magnitude of a vector cannot be negative even though a component can. Finally, write the six-step sequence: draw, choose axes, resolve, operate, reconstruct and verify.

Answer: With east = +x and north = +y, the sign pairs are (+,+), (+,−), (−,+) and (−,−). Magnitude describes size and is non-negative; a component is a signed projection relative to an axis. If either explanation is uncertain, repair it before continuing because later arithmetic will hide the same gap.

Level 1

Foundation questions with worked solutions

1. Scalar or vector?

Classify distance, displacement, speed, velocity, mass, force, energy and acceleration.

Solution: Distance, speed, mass and energy are scalars. Displacement, velocity, force and acceleration are vectors. A vector is not identified by an arrow in the question; its physical definition requires direction and vector combination rules.

2. Equal and negative vectors

Vector A is 12 m east. Describe a vector equal to A and the vector −A.

Solution: Any 12 m east vector representing the same type of quantity is equal in magnitude and direction. −A is 12 m west. It has equal magnitude but opposite direction. Its magnitude is 12 m, not −12 m.

3. Graphical resultant

A student walks 6.0 m east and 8.0 m north. Find distance and displacement.

Solution: Distance = 6.0 + 8.0 = 14.0 m. Displacement components are (6.0, 8.0) m, so R = √(6² + 8²) = 10.0 m. The direction is tan⁻¹(8/6) = 53.1° north of east.

distance = 14.0 m; displacement = 10.0 m at 53.1° north of east

Check: The displacement is shorter than the path and lies in the first quadrant.

Level 2

Component questions with worked solutions

4. Resolve a north-west force

A 24 N force acts 35° north of west. Take east and north as positive.

Solution: West gives a negative x-component; north gives a positive y-component. F_x = −24 cos 35° ≈ −19.7 N and F_y = 24 sin 35° ≈ 13.8 N.

F ≈ (−19.7 î + 13.8 ĵ) N

Check: √(19.7² + 13.8²) ≈ 24.0 N and the signs describe quadrant II.

5. Reconstruct a vector

A velocity has components v_x = −15 m s⁻¹ and v_y = −8 m s⁻¹. Find magnitude and direction.

Solution: v = √(15² + 8²) = 17 m s⁻¹. Both components are negative, so the velocity points south-west. The reference angle is tan⁻¹(8/15) ≈ 28.1°.

v = 17 m s⁻¹, 28.1° south of west

Check: The horizontal component is larger, so the direction should be closer to west than south.

6. Angle measured from north

A 40 m displacement is 25° east of north. Find its components.

Solution: Because the angle begins at north, the north component is adjacent: y = 40 cos 25° ≈ 36.3 m. The east component is opposite: x = 40 sin 25° ≈ 16.9 m. Both are positive.

Learning point: “x uses cosine” is not a rule. Adjacent uses cosine; the reference axis decides which component is adjacent.

Level 3

Resultant and subtraction questions

7. Three displacements in Kathmandu

A rider travels 5.0 km east, 4.0 km north and 2.0 km west. Find the resultant displacement.

Solution: R_x = 5.0 − 2.0 = 3.0 km; R_y = 4.0 km. R = √(3² + 4²) = 5.0 km. Direction = tan⁻¹(4/3) = 53.1° north of east.

Check: Westward travel reduces but does not reverse the east component.

8. Two non-perpendicular forces

A = 18 N east. B = 12 N at 120° counter-clockwise from east. Find A + B.

Solution: A = (18,0) N. B_x = 12 cos 120° = −6.0 N and B_y = 12 sin 120° ≈ 10.4 N. R = (12.0,10.4) N. Magnitude ≈ 15.9 N and direction ≈ 40.9° north of east.

Check: The answer lies between |18−12| = 6 N and 30 N. Its positive components match the first quadrant.

9. Vector subtraction

For A = 4î − 3ĵ and B = −2î + 5ĵ, find A − B.

Solution: A − B = [4 − (−2)]î + (−3 − 5)ĵ = 6î − 8ĵ. Magnitude = 10. The direction is tan⁻¹(8/6) = 53.1° south of east.

Reverse check: (A − B) + B = (6,−8) + (−2,5) = (4,−3) = A.

Operations with meaning

Dot and cross product practice

10. Work from a dot product

A 30 N force acts at 60° to a 5.0 m displacement. Find the work done by this force.

Solution: W = F · s = Fs cos θ = 30 × 5.0 × cos 60° = 75 J. Only the force component along displacement contributes.

11. Compare the products

Two vectors have magnitudes 6 and 8 and an angle of 30° between them. Find the dot-product value and cross-product magnitude.

Solution: A · B = 6 × 8 × cos 30° ≈ 41.6, a scalar. |A × B| = 6 × 8 × sin 30° = 24, with direction perpendicular to their plane by the right-hand rule. Units depend on the physical quantities represented.

Check: At 30°, cosine exceeds sine, so the dot value should exceed the cross magnitude for equal AB.

Timed transfer

12-minute challenge without worked steps

A boat moves 4.0 m s⁻¹ north relative to water while the river flows 3.0 m s⁻¹ east. Find ground velocity.
Resolve 50 N at 210° measured counter-clockwise from +x.
Given P = 2î + 7ĵ and Q = −4î + ĵ, find P + Q, P − Q and P · Q.
Explain why two vectors of 10 N can have any resultant from 0 N to 20 N.

Answers: (1) 5.0 m s⁻¹, 53.1° north of east. (2) approximately (−43.3î − 25ĵ) N. (3) −2î + 8ĵ; 6î + 6ĵ; −1. (4) changing the angle changes the resultant from opposite-direction cancellation to same-direction addition.

Use the PhET Vector Addition simulation to test only after predicting each result. Move one vector at a time and explain why components or the resultant changed.

Error correction

Common errors this set is designed to expose

Unsigned components

Write direction signs before numbers. A calculator returns a magnitude-like decimal even when physics requires a negative component.

Reference-angle confusion

Draw the axis from which the angle begins. Adjacent uses cosine and opposite uses sine.

Incomplete direction

An answer such as 36° is ambiguous. State north of west, south of east or a clearly defined bearing.

No independent check

Use quadrant, possible magnitude range, recombination or reverse operation—not the same arithmetic twice.

For online or physical NEB tuition, call 9846662070. Bring your attempted page and error classifications so support can target the decision that failed.

Frequently asked questions

Questions about the Vectors practice set

How should I score this Vectors practice set?

Award yourself credit for the diagram and axes, correct signed components, the operation, magnitude, direction with reference, unit and an independent check—not only the final number.

What score shows I am ready to move on?

A useful target is at least 80% on a closed-book mixed attempt plus the ability to explain every correction the next day.

Why do I get the right magnitude but wrong direction?

A squared magnitude can hide component signs. Inspect the signs of the resultant components before using inverse tangent and report the correct quadrant.

Should I use graphical or component addition?

Use graphical addition to understand and estimate the result. Components are usually more precise and scale better to several vectors.

How should I revise wrong answers?

Classify the error, write a prevention rule, then solve a changed version after a delay. Copying the correct steps immediately is not yet mastery.

Where can I get help with NEB Class 11 Vectors?

For current online or physical tuition options, call 9846662070 and confirm the timetable, teacher availability, class mode and fees directly.

References and next steps

Sources and related study guides

Continue with the Class 11 Physics revision roadmap and use the Kinematics guide to apply displacement, velocity and acceleration vectors to motion. Sources and scope were checked on 2 August 2026; follow current CDC, NEB and college instructions if assessment requirements change.

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