Cheat sheet · JEE Preparation Mathematics

Vector Algebra cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

Course

Subject

Chapter

JEE · Mathematics

Cheat sheet

Class 12 · Chapter 10Vector Algebra

Dot product → a number (cos); cross product → a vector (sin).

$\vec a = a_1\hat i + a_2\hat j + a_3\hat k$ , $|\vec a| = \sqrt{a_1^2 + a_2^2 + a_3^2}$ .
Direction cosines l, m, n: l² + m² + n² = 1.
Section formula: $\dfrac{m\vec b + n\vec a}{m + n}$ .

\vec a\cdot\vec b = |a||b|\cos\theta = a_1b_1 + a_2b_2 + a_3b_3

|\vec a\times\vec b| = |a||b|\sin\theta

\vec a\times\vec b = \begin{vmatrix}\hat i & \hat j & \hat k\\ a_1 & a_2 & a_3\\ b_1 & b_2 & b_3\end{vmatrix}

Projection of $\vec a$ on $\vec b$ : $\dfrac{\vec a\cdot\vec b}{|\vec b|}$ .
Area of parallelogram $= |\vec a\times\vec b|$ ; triangle $= \tfrac12|\vec a\times\vec b|$ .

Remember: Magnitude | dot vs cross | projection | areas

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