How would I calculate the unit vectors here? What is the appropriate way to solve this?
I do not completely understand which approach to take. Thanks!
2026-04-13 04:22:27.1776054147
unit vector orthagonal to two vectors
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Cross-product is good in 3D. Another approach is to start by trying to find numbers $x,y,z$ not all $0$ such that $4x+5y+2z=0$ and $x-3z=0$.
We have one degree of freedom here. In this case, use the simple second equation and put $z=1$. Then $x=3$. The first equation now gives $y=-\frac{14}{5}$.
To avoid fractions, multiply everything by $5$. We get $(15,-14,5)$.
To get a unit vector, divide by $\sqrt{x^2+y^2+z^2}$.
For the other answer, multiply everything by $-1$.