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📰 Solution: Two vectors are orthogonal if their dot product equals zero. Compute the dot product: $ x \cdot 2 + 3 \cdot (-x) = 2x - 3x = -x $. Set this equal to zero: $ -x = 0 $. Solving gives $ x = 0 $. \boxed{0} 📰 Question: Determine the minimum value of $ (\tan x + \cot x)^2 $ for $ x $ in the domain where $ \tan x $ and $ \cot x $ are defined. 📰 Solution: Expand $ (\tan x + \cot x)^2 = \tan^2 x + 2 \tan x \cot x + \cot^2 x $. Simplify using $ \tan x \cot x = 1 $: $ \tan^2 x + 2 + \cot^2 x $. Use identity $ \tan^2 x + \cot^2 x = (\tan x - \cot x)^2 + 2 $, so expression becomes $ (\tan x - \cot x)^2 + 4 $. The minimum occurs when $ \tan x = \cot x $, i.e., $ x = \frac{\pi}{4} + k\frac{\pi}{2} $, giving $ 0 + 4 = 4 $. \boxed{4} 📰 South Charleston Recreation Center 5349910 📰 Regn Stock Price 8190600 📰 Guilty Of Being Thats Not My Neighbordiscover The Secret Behind Neighborly Tension 8727777 📰 Third Watch Finally Breaks The Silenceyou Must See This Moment 5685501 📰 5Currency Aed To Rupees You Need To Convert Before This Impact Hits Hard 4068784 📰 How A Simple Carpet Carpet Cleaner Transforms Your Cars Interior Beyond Compare 7375010 📰 You Wont Guess What Designasters Are Saying About These Black Lanvins 7887353 📰 Arable Land Definition 6521727 📰 How A Single Detail In The Sole F63 Treadmill Is Making Everyone Talk About It 1542708 📰 How To Retire Early 9441974 📰 Add More Chaos Top 5 Online 3 Player Games You Have To Try Asap 6306938 📰 Apple Tv Generations 7799787 📰 Find Out What Your Mp3S Are Actually Saying After Merging 1534560 📰 Golden Corral Veterans Day Meal 3923562 📰 Oura Ring Side Effects 6500383