H2 Math : Vectors

Flying grenade SG

For vectors : planes,

one of the specific instructional objectives states this " interpret and find equations of planes in the cartesian form, scalar product form, and parametric form , and convert the equations from one form to another "

Qn : how to convert the abovementioned forms into parametric form?? How to split a normal vector into two vectors perpendicular to the normal vectors (other than obnoxiously difficult guess and check method)?

eagle SG

A normal vector can split into infinite sets of two perpendicular vectors.

Econsphdtutor SG

Just remember that u⊥v ⇔ u·v = 0 .

Example: Given u = (1, 3, 4), I can easily think of vectors that are perpendicular. I simply set v₃ = 0, then think: What should I set v₁ and v₂ to be, in order that

u₁v₁ + u₂v₂ + u₃v₃ = 0?

Simple, just pick v₁ = -3 and v₂ = 1. So v = (-3, 1, 0) is ⊥ to u.

We can similarly and easily also show that the following two vectors are also ⊥ to u:

w = (-4, 0, 1), t = (0, -4, 3).

Please see my free H2 Mathematics Textbook for more.