A vector is a quantity that has both magnitude and direction. Vectors are represented by a directed line segment (or arrow) with an initial point P and terminal point

NJIT Physics 111 Formula Sheet Chapter 1:Vectors and Mathematics Formulas Vector magnitude: | ⃗A| = q q A2 + A2 y or A2 + A2 y + A2 z x x Ay Vector direction: tan Dot Product: …

For a scalar r 0 and a vector c 2 R3, the equation kx ck2 = r2 yields a sphere of radius r centered at c. For a scalar r 0 and vectors c; n 2 R3 with knk = 1, the equation kn cylinder of radius r …

Flux of vector Fields through explicitly defined surfaces S given by z = g ( x , y ) for ( x , y ) ∈ R : ∫∫ = ∫∫ F n dS F < − g x , − g y ,1 > dA where F ( x , y , z ) is a vector field.

A vector V is determined by its length, V and its direction, which we can describe by the angle q that V makes with the horizontal (see figure 13.4). In this figure, we have realized V as the …

SELECTED FORMULAS FOR VECTOR CALCULUS. DERIVATIVES. r= i. @ @x. + j. @ @y. + k. @ @z. (\del" or \nabla" ooperator) F(x;y;z)=F. 1(x;y;z)i +F. 2(x;y;z)j +F. 3(x;y;z)k. …

Vector Formulas a (bxc)= ax (b x c) — (axb) (cxd)= VxVlþ= V (Vxa) Vx(Vxa) v. ova) - vx(a b. (ax b) (a c)b—(a b)c (a c)(b d)—(a d)(b c) o o • a)-V2a b • (Vxa)-a • (Vxb) If x is the coordinate of a …