exam Maths Puzzle Numerical Ability

How can I proove that, given a triangle ABC in rn, the perpenticulars from each side to a vertex meet in the orthocenter, BUT through vectors? Thanks!!:D

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exam Other Question

Simplify so that no negative exponents appear;
(3r^2)^2r^-5
______________(2r^-6)^2
r^-2r^3
I need to solve for all real roots

(x-4)^2=36

and

2(sqrt)(x+4)=3