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📰 \mathbf{w} = \mathbf{w}_\parallel + \mathbf{w}_\perp, \quad \mathbf{w}_\parallel = \frac{\mathbf{v} \cdot \mathbf{w}}{\|\mathbf{v}\|^2} \mathbf{v} = \frac{6}{9} \mathbf{v} = \frac{2}{3} \mathbf{v}. 📰 \|\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. 📰 Cross Stitch Pk 9623897 📰 Shatter Your Expectations My Hero Academia Final Season Revealed Heres Everything 6897307 📰 Lockwood And Co 8304887 📰 Video Proves It Takes Only 2 Minutes Heres The Fastest Method Ever 1193279 📰 Dragon Ball R34 Unleash The Wildest Sequels Youve Never Seen 2663890 📰 Define Immolation 8605534 📰 You Wont Believe What Happens When Dogs Munch On Raisinsshock That No Vet Wants To Share 8594305 📰 Seattle Television Listings 6676997 📰 Symptoms Of Autism In Adults 5096903 📰 This Simple Tip Transformed My Biz Mail Gametry It Before Its Gone 8953355 📰 Sp 500 Index Fund Price Drops To Rock Bottombuy Before It Soars Again 4689604 📰 Museums In My Area 6301571 📰 You Wont Believe What Oikos Pro Used To Change Your Entire Energy Game 162966 📰 Only X Of Travelers Know This Stunning Hudson River Map Heres Why 2094970 📰 Broaden Your Investments Broadridge Stock Shows Unstoppable Momentumdont Miss Out 4216825