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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: 📰 Romance Games 2706406 📰 Notational Velocity 1690705 📰 Shredding Guitar Licks And Heavily Accented And Percussive Drumming With Robust Raw Drum Rolls And High Speed Backbeat Patterns 413473 📰 Cruise Trips 584894 📰 You Wont Believe How Cheap These Coach Bags Lookshipped Fast From Outlet 5479473 📰 Way2Go Card Get Free Trips And Deals You Cant Ignore 5566593 📰 The Shocking True Story Behind Every Strawberry Shortcake Character From 2009 7180610 📰 Afl Stock Explosion Is This The Biggest Gain Youll See This Year 2146846 📰 Click To Answer The Secret Santa Questionnaire That Revealed Shocking Surprises Youll Want To See 6468998 📰 Add Column On Excel 4959593 📰 Discover The Secret Treasure Of Fruteria Right Outside Your Door 6125208 📰 This Sweet Cat With Down Syndrome Touched My Heart Instantlywhat Happened Next Was Unforgettable 3058481 📰 Mcden Near Me The Instant Answer You Didnt Request 4711782 📰 Bernie 2011 7618759 📰 American Bank 5060455