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📰 \|\mathbf{w}_\perp\|^2 = \|\mathbf{w}\|^2 - \|\mathbf{w}_\parallel\|^2 = 16 - \left(\frac{2}{3}\right)^2 \cdot 9 = 16 - 4 = 12. 📰 Now, \(\mathbf{u} \cdot \mathbf{w} = \mathbf{u} \cdot \mathbf{w}_\parallel + \mathbf{u} \cdot \mathbf{w}_\perp = \mathbf{u} \cdot \left(\frac{2}{3} \mathbf{v}\right) + \mathbf{u} \cdot \mathbf{w}_\perp = \frac{2}{3} (\mathbf{u} \cdot \mathbf{v}) + \mathbf{u} \cdot \mathbf{w}_\perp = \frac{2}{3}(1) + \mathbf{u} \cdot \mathbf{w}_\perp = \frac{2}{3} + \mathbf{u} \cdot \mathbf{w}_\perp. 📰 Since \(\|\mathbf{u} - \mathbf{u} \cdot \mathbf{v} \mathbf{v}\| \geq 0\), the projection of \(\mathbf{u}\) onto the plane perpendicular to \(\mathbf{v}\) satisfies: 📰 You Wont Believe What Jane Dobbins Green Compensated For Its Journey Stuns Fans 6114010 📰 Can One Cookie Seed Victory Discover The Mind Blowing Squid Game Cookie Game 5755757 📰 Define Interlocutor 2932303 📰 Tesla Puts Exposedexperts Warn This Hidden Bet Could Trigger A Mega Market Shift 5873763 📰 How Much Is A Movie Ticket 707346 📰 How To Reduce Font Size In Windows 6915605 📰 Purple Hyacinth 4970174 📰 Strauss Legend Revealed The Ultimate Duck Pokmon That Threatens Pokmon Land 3073982 📰 Vessel 4671133 📰 Unravel The Legend The Order Of The Virtuous Blood Shocks History Secretsexposed 9692666 📰 Alexandrite Engagement Ring The Rare Gem That Changed This Brides Life Forever 2568711 📰 Finally Revealed How To Add A Drop Down List In Excel Like A Pro 7356604 📰 Amir Arison 5344115 📰 Ascent Of Ashes 2958677 📰 The Dot On A Domino Hides A Secret No One Expected 2647087