➡️ Vectors 2D Addition & Dot Product Visualizer
VectorsWhat's happening? R = A + B. The parallelogram law shows vector addition geometrically. Dot product measures projection, cross product measures perpendicularity.
Vectors: 4-5 questions every year.
JEE tests addition, dot/cross product, angle, projection.
Key formulas
Vectors (2D) Formulas
Addition
R = A + B, Rx = Ax+Bx
Component-wise
Dot product
A.B = |A||B|cos(theta)
Scalar. Zero if perpendicular
Cross product
|AxB| = |A||B|sin(theta)
Vector. Zero if parallel
Magnitude
|A| = sqrt(Ax^2+Ay^2+Az^2)
3D Pythagorean
Step-by-step problem solving
How to solve maths problems in JEE
- Express in components
- Add: add components
- Dot: multiply and sum
- Angle: cos(theta) = A.B/(|A||B|)
Common JEE mistakes
What students get wrong
Cross product order
AxB = -(BxA). Not commutative!
Dot vs cross
Dot = scalar, Cross = vector
Unit vectors
i.i=1, i.j=0, ixj=k
Angle range
theta between 0 and pi
FAQs
Vectors (2D) Questions
Angle between vectors?
cos(theta) = A.B/(|A||B|)
Dot product zero?
Perpendicular or one is zero
Cross product 3D?
Determinant with i,j,k or |A||B|sin(theta) right-hand rule
Unit vector?
vector / |vector|. Magnitude 1.