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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: 📰 Why Every Sniper Movie Is A Life Changing Action Experience You Need To Watch 127944 📰 How Kwl Hub Boosted Engagement By 300Heres How You Can Too 4078107 📰 Proven Secrets To Winning At Pinochle Classicsecrets Legends Wont Tell 1978057 📰 Lotto Washington 7087928 📰 Angelaincolleges Shocking Testdid They Really Require This One Student Reveals All 6646307 📰 Discover The Breathtaking Skyward Alpine Secret No One Talks About 4532088 📰 Notre Dame Football Delay 5735949 📰 Shocked By Kalluto Zoldycks Hidden Powersinside His Zombie Dominion 3907266 📰 Pre Owned Verizon 9514597 📰 Utc Where The World Stops And Time Becomes Irrelevantunlock The Mystery Now 3655170 📰 Marsh And Mclennan Stock Price 9982856 📰 Price Of Ebay Stock Today Is This Your Last Chance To Buy Before It Spikes 5924996 📰 Yosuke Hanamuras Hidden Talent How His Layers Shocked Fans Forever 311865 📰 Stop Waiting How Uab Patient Portal Gives You Full Control Over Your Care 9940797 📰 Future Value 5000 Times 1 00112 3166695