Vectors Flashcards
1
Q
What is the angle between a line and a plane?
A
Angle Alpha is worked out using the standard form and then doing 90 - theta
𝑎. 𝑏 = 𝑎 𝑏 𝑐𝑜𝑠𝜃
𝑏. 𝑛 = 𝑏 𝑛 𝑐𝑜𝑠𝜃
𝑛1. 𝑛2 = 𝑛1 𝑛2 𝑐𝑜𝑠𝜃
2
Q
What is the angle between two planes?
A
Angle Alpha is worked out the standard way and then doing 180 - theta
𝑎. 𝑏 = 𝑎 𝑏 𝑐𝑜𝑠𝜃
𝑏. 𝑛 = 𝑏 𝑛 𝑐𝑜𝑠𝜃
𝑛1. 𝑛2 = 𝑛1 𝑛2 𝑐𝑜𝑠𝜃
3
Q
What is the equation for the shortest distance between a point and a plane?
A
(x, y, z) . (n1, n2, n3) - d / root(n1^2 + n2^2 + n3^3)
4
Q
What is the equation of a straight line?
A
r = a + λb
5
Q
What is the equation of a plane?
A
r = a + λb + μc, r.n = d
6
Q
What is the cartesian equation of a line?
A
𝜆 = 𝑥 − 𝑎1 / 𝑏1 = 𝑦 − 𝑎2 / 𝑏2 = 𝑧 − 𝑎3 / 𝑏3
