Vectors formulas

Every formula JEE Advanced expects you to know for Vectors, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 30
Subject: Physics
Exam: JEE Advanced
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Vectors, every formula

30 formulas, typeset and free. Print it, or keep it open beside your practice.

Magnitude of a vector
$∣ A ∣ = A_{x}^{2} + A_{y}^{2} + A_{z}^{2}$
Unit vector
$\hat{A} = \frac{A}{∣ A ∣}$
Components of a vector
$A_{x} = A cos θ, A_{y} = A sin θ$
Parallelogram law (resultant)
$R = A^{2} + B^{2} + 2 A B cos θ$
Direction of resultant
$tan α = \frac{B sin θ}{A + B cos θ}$
Maximum resultant
$R_{m a x} = A + B (θ = 0)$
Minimum resultant
$R_{m i n} = ∣ A - B ∣ (θ = 18 0^{\circ})$
Perpendicular vectors' resultant
$R = A^{2} + B^{2} (θ = 9 0^{\circ})$
Position & displacement vector
$A B = b - a$
Distance between two points
$d = ∣ a - b ∣$
Section formula
$r = \frac{n a + m b}{m + n}$
Midpoint
$r = \frac{a + b}{2}$
Dot product (definition)
$A \cdot B = A B cos θ$
Dot product (components)
$A \cdot B = A_{x} B_{x} + A_{y} B_{y} + A_{z} B_{z}$
Angle via dot product
$cos θ = \frac{A \cdot B}{A B}$
Perpendicular condition
$A \cdot B = 0 \Leftrightarrow A ⊥ B$
Projection
$proj = \frac{A \cdot B}{B}$
Unit-vector dot products
$\hat{i} \cdot \hat{i} = 1, \hat{i} \cdot \hat{j} = 0$
Cross product (definition)
$A \times B = A B sin θ \overset{n}{^}$
Cross product (determinant)
$A \times B = \hat{i} A_{x} B_{x} \hat{j} A_{y} B_{y} \hat{k} A_{z} B_{z}$
Magnitude of cross product
$∣ A \times B ∣ = area of parallelogram$
Parallel condition
$A \times B = 0 \Leftrightarrow A ∥ B$
Anticommutativity
$A \times B = - (B \times A)$
Unit-vector cross products
$\hat{i} \times \hat{j} = \hat{k}, \hat{j} \times \hat{k} = \hat{i}, \hat{k} \times \hat{i} = \hat{j}$
Scalar triple product
$[A B C] = A \cdot (B \times C)$
Coplanarity
$[A B C] = 0$
Vector triple product
$A \times (B \times C) = (A \cdot C) B - (A \cdot B) C$
Lami's theorem
$\frac{A}{sin α} = \frac{B}{sin β} = \frac{C}{sin γ}$
three concurrent forces
|A+B|²
$∣ A + B ∣^{2} = A^{2} + B^{2} + 2 A B cos θ$
Work (dot product)
$W = F \cdot d$

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Vectors formulas

Vectors, every formula

Magnitude of a vector

Unit vector

Components of a vector

Parallelogram law (resultant)

Direction of resultant

Maximum resultant

Minimum resultant

Perpendicular vectors' resultant

Position & displacement vector

Distance between two points

Section formula

Midpoint

Dot product (definition)

Dot product (components)

Angle via dot product

Perpendicular condition

Projection

Unit-vector dot products

Cross product (definition)

Cross product (determinant)

Magnitude of cross product

Parallel condition

Anticommutativity

Unit-vector cross products

Scalar triple product

Coplanarity

Vector triple product

Lami's theorem

|A+B|²

Work (dot product)

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