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@0xcaff
Last active Feb 20, 2017
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Calculus III Project I
==> question2a.txt <==
Distance: 89/sqrt(1635)
==> question2b.txt <==
Distance: 40/sqrt(104)
==> question2c.txt <==
Distance: 64/sqrt(222)
==> question3.txt <==
Equation: -5(x - 3) + -10(y + 1) + 5(z - 2) = 0
==> question4.txt <==
Equation: -5(x - 4) + -10(y - 0) + 5(z - 3) = 0
==> question5.txt <==
Equation: -5(x - 5) + -10(y - 1) + 5(z - 4) = 0
==> question6.txt <==
Equation: -5(x - 6) + -10(y - 2) + 5(z - 5) = 0
==> question7.txt <==
Equation: -5(x - 7) + -10(y - 3) + 5(z - 6) = 0
==> question8.txt <==
Area: sqrt(150)
==> question9.txt <==
Area: sqrt(150)
==> question10.txt <==
Area: sqrt(150)
==> question11.txt <==
Area: sqrt(150)
==> question12.txt <==
Area: sqrt(150)
function vector(from, to) {
return {
x: to.x - from.x,
y: to.y - from.y,
z: to.z - from.z,
};
}
function crossProduct(u, v) {
return {
x: u.y * v.z - v.y * u.z,
y: -(u.x * v.z - v.x * u.z),
z: u.x * v.y - v.x * u.y,
};
}
function signed(num) {
if (num > 0) {
return "+ " + num;
} else {
return "- " + (-num).toString();
}
}
function mag2(vec) {
return vec.x * vec.x + vec.y * vec.y + vec.z * vec.z;
}
// // question 8
// const a = {x: 3, y: -1, z: 2};
// const b = {x: 2, y: 1, z: 5};
// const c = {x: 1, y: -2, z: -2};
// // question 9
// const a = {x: 4, y: 0, z: 3};
// const b = {x: 3, y: 2, z: 6};
// const c = {x: 2, y: -1, z: -1};
// // question 10
// const a = {x: 5, y: 1, z: 4};
// const b = {x: 4, y: 3, z: 7};
// const c = {x: 3, y: 0, z: 0};
// // question 11
// const a = {x: 6, y: 2, z: 5};
// const b = {x: 5, y: 4, z: 8};
// const c = {x: 4, y: 1, z: 1};
// question 12
const a = {x: 7, y: 3, z: 6};
const b = {x: 6, y: 5, z: 9};
const c = {x: 5, y: 2, z: 2};
const AB = vector(a, b);
const AC = vector(a, c);
const n = crossProduct(AB, AC);
console.log(`Area: sqrt(${mag2(n)})`);
function vector(from, to) {
return {
x: to.x - from.x,
y: to.y - from.y,
z: to.z - from.z,
};
}
function crossProduct(u, v) {
return {
x: u.y * v.z - v.y * u.z,
y: -(u.x * v.z - v.x * u.z),
z: u.x * v.y - v.x * u.y,
};
}
function signed(num) {
if (num > 0) {
return "+ " + num;
} else {
return "- " + (-num).toString();
}
}
// question 3
const a = {x: 3, y: -1, z: 2};
const b = {x: 2, y: 1, z: 5};
const c = {x: 1, y: -2, z: -2};
// question 4
// const a = {x: 4, y: 0, z: 3};
// const b = {x: 3, y: 2, z: 6};
// const c = {x: 2, y: -1, z: -1};
// question 5
// const a = {x: 5, y: 1, z: 4};
// const b = {x: 4, y: 3, z: 7};
// const c = {x: 3, y: 0, z: 0};
// question 6
// const a = {x: 6, y: 2, z: 5};
// const b = {x: 5, y: 4, z: 8};
// const c = {x: 4, y: 1, z: 1};
// question 7
// const a = {x: 7, y: 3, z: 6};
// const b = {x: 6, y: 5, z: 9};
// const c = {x: 5, y: 2, z: 2};
const AB = vector(a, b);
const AC = vector(a, c);
const n = crossProduct(AB, AC);
console.log(`Equation: ${n.x}(x ${signed(-a.x)}) + ${n.y}(y ${signed(-a.y)}) + ${n.z}(z ${signed(-a.z)}) = 0`);
function crossProduct(u, v) {
return {
x: u.y * v.z - v.y * u.z,
y: -(u.x * v.z - v.x * u.z),
z: u.x * v.y - v.x * u.y,
};
}
function dotProduct(u, v) {
return u.x * v.x + u.y * v.y + u.z * v.z;
}
function mag2(vec) {
return vec.x * vec.x + vec.y * vec.y + vec.z * vec.z;
}
function vector(from, to) {
return {
x: to.x - from.x,
y: to.y - from.y,
z: to.z - from.z,
};
}
function abs(num) {
if (num > 0) {
return num;
} else {
return -num;
}
}
// question 2.a
const l1 = {x: 5, y: 5, z: -4};
const l2 = {x: 1, y: 8, z: -3};
const p = {x: 4, y: 5, z: 1};
const q = {x: 4, y: -6, z: 7};
// question 2.b
// const l1 = {x: 2, y: 4, z: 6};
// const l2 = {x: -1, y: 1, z: 1};
//
// const p = {x: 0, y: 0, z: 0};
// const q = {x: 1, y: 4, z: -1};
// // question 2.c
// const l1 = {x: 3, y: -1, z: 1};
// const l2 = {x: 4, y: 1, z: -3};
//
// const p = {x: 0, y: 2, z: -1};
// const q = {x: 1, y: -2, z: -3};
const pq = vector(p, q);
const n = crossProduct(l1, l2);
// project pq onto n then take magnitude
console.log(`Distance: ${abs(dotProduct(n, pq))}/sqrt(${mag2(n)})`);
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