Vector Algebra Class 12 Maths Notes – Formulas & Quick Revision

Vector Algebra mein dot-cross product, projection aur vectors ki geometry aati hai — 3D ka base. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Vector Algebra

• |a| = √(x² + y² + z²)
• Unit vector: â = a/|a|
• Section formula: (mb + na)/(m + n)
• Dot: a·b = |a||b|cosθ = x₁x₂ + y₁y₂ + z₁z₂
• Projection of a on b = a·b/|b|
• Cross: a×b = |a||b|sinθ n̂ (determinant se nikalo)
• Area of parallelogram = |a×b|; triangle = ½|a×b|
• a·b = 0 ⟹ perpendicular; a×b = 0 ⟹ parallel

Quick Revision Points

• Dot product scalar hai, cross product vector
• a×b ⊥ dono a aur b ke
• î×ĵ = k̂ (cyclic); ĵ×î = −k̂
• Angle between vectors: cosθ = a·b/(|a||b|)
• Cross product ka determinant method mein signs dhyan se

FAQ

Dot vs cross kab use karu?

Angle/projection → dot; area/perpendicular vector → cross. PDF mein use-case table hai.

3D se pehle ye chapter zaroori hai?

Haan — 3D geometry ke saare formulas vectors par hi likhe hain.

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