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Vectors (Physics) formula sheet

Every formula in the Vectors (Physics) chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 28 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Scalars, vectors and components

Magnitude and unit vector
5× asked, last 2025
∣A⃗∣=Ax2+Ay2+Az2,A^=A⃗∣A⃗∣|\vec A|=\sqrt{A_x^2+A_y^2+A_z^2},\qquad \hat A=\frac{\vec A}{|\vec A|}
A^\hat A has size 1 and no unit. A vector of size CC along B⃗\vec B is CB^C\hat B.
Position and displacement
r⃗=xi^+yj^+zk^,PQ⃗=r⃗Q−r⃗P\vec r=x\hat i+y\hat j+z\hat k,\qquad \vec{PQ}=\vec r_Q-\vec r_P
Final minus initial. Unit vector along it: PQ⃗/∣PQ⃗∣\vec{PQ}/|\vec{PQ}|.
Components in a plane
5× asked, last 2024
Ax=Acos⁡θ,Ay=Asin⁡θ,tan⁡θ=AyAxA_x=A\cos\theta,\quad A_y=A\sin\theta,\qquad \tan\theta=\frac{A_y}{A_x}
θ\theta from the +x+x axis; cos goes with the axis the angle starts from. Quadrant from the signs.
Direction cosines
1× asked, last 2021
cos⁡α=AxA,  cos⁡β=AyA,  cos⁡γ=AzAcos⁡2α+cos⁡2β+cos⁡2γ=1\begin{aligned}&\cos\alpha=\frac{A_x}{A},\ \ \cos\beta=\frac{A_y}{A},\ \ \cos\gamma=\frac{A_z}{A}\\&\cos^2\alpha+\cos^2\beta+\cos^2\gamma=1\end{aligned}
Angles with the xx, yy, zz axes; they are the components of A^\hat A.
Resolving along two given lines
1× asked, last 2021
P1=Psin⁡βsin⁡(α+β),P2=Psin⁡αsin⁡(α+β)P_1=\frac{P\sin\beta}{\sin(\alpha+\beta)},\qquad P_2=\frac{P\sin\alpha}{\sin(\alpha+\beta)}
Lines at α\alpha and β\beta from P⃗\vec P, on opposite sides. At 90∘90^\circ: Pcos⁡αP\cos\alpha, Psin⁡αP\sin\alpha.

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Practise Vectors (Physics)

23 more formulas in 4 topics

Vector addition and subtraction, Equilibrium of concurrent forces, Dot product and Cross product. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Vector addition and subtraction

  • Resultant of two vectors8×
  • Range of the resultant
  • Difference of two vectors9×
  • Two vectors of equal size5×
  • Size condition as a dot product
  • Triangle and polygon laws4×
  • Regular polygon

Equilibrium of concurrent forces

  • Condition for equilibrium2×
  • Three forces can balance only if
  • Lami's theorem

Dot product

  • Dot (scalar) product10×
  • Angle between two vectors
  • Perpendicular vectors6×
  • Component and projection3×
  • Work and power1×

Cross product

  • Cross (vector) product7×
  • Unit vector products
  • Parallel vectors3×
  • Unit vector normal to a plane2×
  • Area from a cross product
  • Torque and angular momentum3×
  • Dot and cross together1×
  • Scalar triple product1×

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