Core5 mapped NDA questions
Build the idea
Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.
Concept
A vector has both magnitude and direction. The dot product yields a scalar (and the angle between vectors); the cross product yields a vector perpendicular to both (and the area of a parallelogram).
Vectors model forces, displacements and geometric relations.
Key Points & Formulas
- Magnitude of a î + b ĵ + c k̂ = √(a²+b²+c²).
- Dot product a·b = |a||b|cosθ = a₁b₁ + a₂b₂ + a₃b₃.
- Cross product magnitude |a×b| = |a||b|sinθ.
- a·b = 0 ⇒ perpendicular; a×b = 0 ⇒ parallel.
Worked Example
Q. Find the angle between a = î + ĵ and b = ĵ + k̂.
a·b = (1)(0)+(1)(1)+(0)(1) = 1.
|a| = √2, |b| = √2, so cosθ = 1/(√2·√2) = 1/2.
θ = 60°.