week 10

Question 1

Scalar triple product

Answer 1

(axb).c or a.(cxb) .if equals zero then a,b,c are coplanar

Question 2

congruence

Answer 2

a is congruent to b mod m if b - a is divisible by m

Question 3

every number is congruent to ___ mod m

Answer 3

0,1,2, …. , m-1

Question 4

Congruencce divisions

Answer 4

if p and a= are coprime then xa = ya modp implies x= y modp

Question 5

operations in Zn

Answer 5

if x and y in Zn x + y
= k such that x+ y is congruent to kmodm

Question 6

Vector equation

Answer 6

r = r_0 + tV. r is a point on the line defined using a point on the line L r_0. This is a position vector. then V is a vector parallel to L, t is an arbritary variable to describe all r.

Question 6

parametric and cartesian

Answer 6

individual equtions or x y and z, then joined together by solving fr t and equating. can be used too find V and r_0 relatively easily. if V is the same for two vectors, they are parallel or equal. IF not they interact or are skew

Question 7

plane equation

Answer 7

nr = nr_0. n is an orthogonal vector, r is a general expression for a point, and r0 is an example point.

Question 8

intersection of planes

Answer 8

angle between planes will be equal too angle between normals. if planes aint parallel they will interacti in line, where V = n1Xn2