Quiz 1 Prep

Question 1

What the general principle from describing dimensions of things?

Answer 1

Everytime you add a dimension, you remove an equation:
ex. to describe something thats one dimension requires 2 equations and two dimensions requires 1 equation.

Question 2

Circle Formula for R^2

Answer 2

(x-a)^2 + (y-b)^2 = r^2

Question 3

Circle Formula for R^3

Answer 3

(x-a)^2 + (y-b)^2 + (x-c)^2= r^2. It’s actually a sphere in 3D. We know this b/c all the coefficents are one.

Question 4

What’s a unit vector?

Answer 4

any vector with a length of 1. Ex <3/5, 4/5> and <-2/3, 2/3, 1/3> You can try with distance formula

Question 5

Idea behind vector addition and subtraction?

Answer 5

when you add or subtract, each coordinate corresponds to another. a + b = <a_1+b_1, a_2 + b_2, a_3+b_3>

Question 6

idea behind scalar multiplication

Answer 6

K∈R. ka = <ka_1, ka_2, ka_3>

Question 7

when are two vectors parallel?

Answer 7

when they point the exact same or opposite direction and if there is a k ≠ 0 so that vector v =k(vector w)

Question 8

when do 2 vectors point in the same direction?

Answer 8

when there is a k > 0 so that vector v =k(vector w). (When one is scaled of another)

Question 9

given a vector v and a number, k > 0, what is the vector of length K in the same direction as vector v?

Answer 9

new vector (w) = (k/length of vector v) vector v

Question 10

Formula for dot product

Answer 10

v = <a,b,c> w= <x,y,z>
ax + by + cz <- Don’t expect a vector, expect a number.

Question 11

how do you find the angle b/w two vectors

Answer 11

vectors v * w = lengths of vectors v * w * cos(θ). defining characteristic of the dot product

Question 12

when vectors orthogonal?

Answer 12

when the dot product b/w the two = 0/meet at a right angle

Question 13

what is a position vector?

Answer 13

vector that starts at the origin (0,0,0)

Question 14

standard unit vectors

Answer 14

i = <1, 0, 0>
j = <0, 1, 0>
k = <0, 0, 1>