Topic explanation · Public Library

Read the topic explanation, then try Quiz or Practice to check understanding.

Classroom-style explanation with key points, examples, and study tools for each topic.

Dot Product in Component Form

Mathematics · Class 11

i·i=1, i·j=0. Expand (x1 i+...)·(y1 i+...). Distributive: a·(b+c)=a·b+a·c. Commutative: a·b=b·a.

sum ai bi
a·b = |a||b| cos theta
also sum of products of components
scalar result
DOT PRODUCT IN COMPONENT FORM: i·i=1, i·j=0. Expand (x1 i+...)·(y1 i+...). Distributive: a·(b+c)=a·b+a·c. Commutative: a·b=b·a.
COMPONENTS: i·i=1, i·j=0.
WHAT — DOT PRODUCT IN COMPONENT FORM: i·i=1, i·j=0. Expand (x1 i+...)·(y1 i+...). Distributive: a·(b+c)=a·b+a·c. Commutative: a·b=b·a.
WHY — Why it matters: This rule is a separate learning unit inside dot (scalar) product. It can be defined, applied, and c

Right triangle — Dot Product in Component Form — original sketch for this lesson (not copied from a textbook).