week 9

Question 1

vector vs position vector

Answer 1

A vector is the distance between 2 points starting at point 1 terminating at point to, such as vector AB. To mark a position in a plane using a vector we use vectors from the origin. The vector OA is the position vector of the point A. it is the vector starting at 0 and terminating at A

Question 2

unit vector

Answer 2

vector with length one. shares direction. found by dividing a by abs(a). any vector can be written as a sum of the unit vectors i,j and k

Question 3

Orthogonal vectors

Answer 3

2 vectors are orthogonal if theta is 90. This means dot product is zero

Question 4

directional angles

Answer 4

angle alpha beta and gamma that vector a makes with x, y and z axis respectively. cosalpha = i component/ modulus

Question 5

vector projection of b onto a

Answer 5

how much the vector b goes along vector a by joining a perpendicular from the terminus of b to a

Question 6

if n = m^k then the prime expansion of n

Answer 6

has every prime to a power divisible by k. you can tell if numbers are squares, cubes etc by their prime expansion.

Question 7

diophantine equations

Answer 7

equations in terms of x and y that only consider integer solutions. try to use euclidean, fundamental theorem of algebra or factoring.