Class 11 · Chapter 1

Basic Mathematics & Vectors

Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.

Basic Mathematics & Vectors JEE Notes

4 min read

Fully worked, multi-step problems combining vector algebra and basic calculus — the toolkit-building exercises that JEE Main and JEE Advanced lean on throughout mechanics, beyond the single-step formula questions in the regular DPP.

Illustration 1 — Lami's Theorem, Classic 3-4-5 Forces

Three forces of magnitude 3 N, 4 N, and 5 N keep a particle in equilibrium. Find the angle between the 3 N and 4 N forces.

Illustration 2 — Finding an Unknown Vector from an Equilibrium Condition

Three vectors A = 3î + 4ĵ, B = −2î + ĵ, and C satisfy A + B + C = 0. Find C.

Illustration 3 — Product Rule with a Logarithmic Function

Find dy/dx for y = x³ ln(x), and evaluate it at x = 1.

Illustration 4 — Definite Integral for Total Change

A quantity changes at the rate dQ/dx = 3x² + 2x. Find the total change in Q as x goes from 0 to 2.

Illustration 5 — Dot and Cross Product Together

For vectors A = 4î and B = 2î + 2ĵ, find (a) the angle between them using the dot product, and (b) the area of the parallelogram they form using the cross product.

Illustration 6 — Unit Vector Perpendicular to Two Given Vectors

Find a unit vector perpendicular to both A = î + ĵ and B = ĵ + k̂.

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