6.3 Vector in the Plane

6.3 Vector in the Plane Magnitude Component form Unit Vector

Vector is a Directed Line Segment Terminal point Initial point Magnitude ( or Length): || PQ ||

Let P = (0,0) and Q = (3,4) To find the Magnitude || PQ || Direction (slope) is always important. Slope of

Vectors equality If two vectors equal if they have the same magnitude and direction.

is a vector in standard position Vectors in Standard position have an initial point at the origin (0, 0).

Component Form of a vector P = (p1, p2 ); Q = (q1, q2 ) Which can be labeled by just a letter.

Vector “V” can renamed If || V || = 1, then V is a Unit Vector. || V || = 0 iff V is 0

Find the Component form and Magnitude Let

Vector Operations Scalar Multiplication Let

Vector Operations Vector Addition Let

Parallelogram Law used in Addition of Vectors Graph the Vectors move the tail of one vector to the head of the other vector.

Properties of Vectors U + V = V + U (Comm.) (U + V) + W = U + (V + W) (Asso.) U + 0 = U (Identity) U + (-U) = 0 (Inverse) C(DU)=(CD)U (Comm.) (C + D)U = CU + DU (Dist.) 1(U)=U; 0(U)=0 || cV|| =|c| x ||V||

How to Find the Unit Vector Let

Standard Unit Vector Writing the Unit Vector as Standard Unit Vector. i = j =

Direction Angle of a Unit Vector What is the coordinate of the intersection of the vector and unit circle?

Direction Angle of a Unit Vector What is the slope of the vector? What function Is rise over run?

Direction of a Vector can be found if it is not a Unit Vector

6.3 Vector in the Plane