/sci/ - Science & Math

What are some current universal ongoing debates in the field of compsci so that I can connect more with my admissions tutor.

>inb4muh artificial intelligence

How do I show that the vector equation of a line

[eqn] r = (6, -5, 1) + λ(-1, 2, -3) [/eqn]

is perpendicular to the plane

[eqn] x - 2y + 3z = -9 [/eqn]

I'll start. How in the sweet baby Jesus do you answer my next post

Hey guys... I'll start with some basic trig:

When solving something like 2sin θ + 3cos θ= 1

why would using the form rsin(θ+a) be used instead of just squaring all the variables and converting either cos^2 x to 1-sin^2 x or vice versa?

so that it becomes [eqn] 4sin^2 (θ) + 9cos^2 (θ) = 1 [/eqn]

to

[eqn] 4 - 4cos^2 (θ) + 9cos^2 (θ) = 1 [/eqn]

and solve the following for:

[eqn] 5cos^2 (θ) = -3 [/eqn]

I know its wrong... but why wouldn't it work?
thanks.

I'll start with basic geometry...

Show that the curves y=x^4 - 2 and y=kx^2 intersect for all values of k