https://peda.net/id/2e6870ae6d6 2019-05-03T08:34:54+03:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/72e1888c6d7 2019-05-03T09:55:34+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BOA%7D%3D-2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B%5Coverline%7B%5Ctext%7Bj%7D%7D%5C%20" alt="\overline{OA}=-2\overline{\text{i}}+\overline{\text{j}}\ "/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BOB%7D%3D%5Coverline%7BOA%7D%2B%5Coverline%7BAB%7D%3D2%5Coverline%7B%5Ctext%7Bi%7D%7D-%5Coverline%7B%5Ctext%7Bj%7D%7D" alt="\overline{OB}=\overline{OA}+\overline{AB}=2\overline{\text{i}}-\overline{\text{j}}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5C%20B%3D%5Cleft(2%7B%2C%7D%5C%20-1%5Cright)%5C%20" alt="\ B=\left(2{,}\ -1\right)\ "/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BOC%7D%3D%5Coverline%7BOA%7D%2B%5Coverline%7BAB%7D%2B%5Coverline%7BBC%7D%3D5%5Coverline%7B%5Ctext%7Bi%7D%7D%2B3%5Coverline%7B%5Ctext%7Bj%7D%7D%5C%20" alt="\overline{OC}=\overline{OA}+\overline{AB}+\overline{BC}=5\overline{\text{i}}+3\overline{\text{j}}\ "/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=C%3D%5Cleft(5%7B%2C%7D%5C%203%5Cright)" alt="C=\left(5{,}\ 3\right)"/> 2019-05-03T09:55:34+03:00 https://peda.net/id/569377726d6 2019-05-03T09:50:11+03:00 <a href="https://peda.net/p/oskari.lahtinen/maa4p-vektorit/2gv/231/sieppaa-png#top" title="Sieppaa.PNG"><img src="https://peda.net/p/oskari.lahtinen/maa4p-vektorit/2gv/231/sieppaa-png:file/photo/109669026ce8aa2b5b15a52dc6ad61177603aabb/Sieppaa.PNG" alt="" title="Sieppaa.PNG" class="inline" loading="lazy"/></a><br/> <br/> lasketaan vektoreiden pituudet<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C%5Coverline%7Bv%7D%5Cright%7C%3D2" alt="\left|\overline{v}\right|=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C%5Coverline%7Bu%7D%5Cright%7C%3D%5Csqrt%7B%5Cleft(-4%5Cright)%5E2%2B1%5E2%7D%3D%5Csqrt%7B17%7D" alt="\left|\overline{u}\right|=\sqrt{\left(-4\right)^2+1^2}=\sqrt{17}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C%5Coverline%7Bw%7D%5Cright%7C%3D%5Csqrt%7B%5Cleft(-4%5Cright)%5E2%2B%5Cleft(-1%5Cright)%5E2%7D%3D%5Csqrt%7B17%7D" alt="\left|\overline{w}\right|=\sqrt{\left(-4\right)^2+\left(-1\right)^2}=\sqrt{17}"/><br/> kolmion kaksi sivua on saman pituiset, eli kolmio on tasakylkinen 2019-05-03T09:47:37+03:00 https://peda.net/id/b095d4106d6 2019-05-03T09:44:34+03:00 a)<br/> <a href="https://peda.net/p/oskari.lahtinen/maa4p-vektorit/2gv/230/sieppaa-png#top" title="Sieppaa.PNG"><img src="https://peda.net/p/oskari.lahtinen/maa4p-vektorit/2gv/230/sieppaa-png:file/photo/a8cd907236ea9cfd9e5f399077fa8fc8ff65dcd7/Sieppaa.PNG" alt="" title="Sieppaa.PNG" class="inline" loading="lazy"/></a><br/> <br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BOA%7D%3D-2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B%5Coverline%7B%5Ctext%7Bj%7D%7D" alt="\overline{OA}=-2\overline{\text{i}}+\overline{\text{j}}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BAB%7D%3D3%5Coverline%7B%5Ctext%7Bi%7D%7D-%5Coverline%7B%5Ctext%7Bj%7D%7D" alt="\overline{AB}=3\overline{\text{i}}-\overline{\text{j}}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BOB%7D%3D%5Coverline%7BOA%7D%2B%5Coverline%7BAB%7D%3D3%5Coverline%7B%5Ctext%7Bi%7D%7D-2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B%5Coverline%7B%5Ctext%7Bj%7D%7D-%5Coverline%7B%5Ctext%7Bj%7D%7D%3D%5Coverline%7B%5Ctext%7Bi%7D%7D" alt="\overline{OB}=\overline{OA}+\overline{AB}=3\overline{\text{i}}-2\overline{\text{i}}+\overline{\text{j}}-\overline{\text{j}}=\overline{\text{i}}"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=B%3D%5Cleft(1%7B%2C%7D%5C%200%5Cright)" alt="B=\left(1{,}\ 0\right)"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BAD%7D%3D2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B2%5Coverline%7B%5Ctext%7Bj%7D%7D" alt="\overline{AD}=2\overline{\text{i}}+2\overline{\text{j}}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BOD%7D%3D%5Coverline%7BOA%7D%2B%5Coverline%7BAD%7D%3D-2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B%5Coverline%7B%5Ctext%7Bj%7D%7D%2B2%5Coverline%7B%5Ctext%7Bj%7D%7D%3D3%5Coverline%7B%5Ctext%7Bj%7D%7D" alt="\overline{OD}=\overline{OA}+\overline{AD}=-2\overline{\text{i}}+2\overline{\text{i}}+\overline{\text{j}}+2\overline{\text{j}}=3\overline{\text{j}}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=D%3D%5Cleft(0%7B%2C%7D%5C%203%5Cright)" alt="D=\left(0{,}\ 3\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7BOC%7D%3D%5Coverline%7BOA%7D%2B%5Coverline%7BAB%7D%2B%5Coverline%7BAD%7D%3D-2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B3%5Coverline%7B%5Ctext%7Bi%7D%7D%2B2%5Coverline%7B%5Ctext%7Bi%7D%7D%2B%5Coverline%7B%5Ctext%7Bj%7D%7D-%5Coverline%7B%5Ctext%7Bj%7D%7D%2B2%5Coverline%7B%5Ctext%7Bj%7D%7D%3D3%5Coverline%7B%5Ctext%7Bi%7D%7D%2B2%5Coverline%7B%5Ctext%7Bj%7D%7D" alt="\overline{OC}=\overline{OA}+\overline{AB}+\overline{AD}=-2\overline{\text{i}}+3\overline{\text{i}}+2\overline{\text{i}}+\overline{\text{j}}-\overline{\text{j}}+2\overline{\text{j}}=3\overline{\text{i}}+2\overline{\text{j}}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=C%3D%5Cleft(3%7B%2C%7D%5C%202%5Cright)" alt="C=\left(3{,}\ 2\right)"/></div> 2019-05-03T09:35:49+03:00 https://peda.net/id/db6d2a226d6 2019-05-03T09:29:51+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cleft(1%7B%2C%7D2%5Cright)" alt="A=\left(1{,}2\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=B%3D%5Cleft(17%7B%2C%7D-12%5Cright)" alt="B=\left(17{,}-12\right)"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Cfrac%7B1%2B17%7D%7B2%7D%7B%2C%7D%5C%20%5Cfrac%7B2-12%7D%7B2%7D%5Cright)%3D%5Cleft(9%7B%2C%7D-5%5Cright)" alt="\left(\frac{1+17}{2}{,}\ \frac{2-12}{2}\right)=\left(9{,}-5\right)"/></div> <div>b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cleft(-5%7B%2C%7D1%5Cright)" alt="A=\left(-5{,}1\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=B%3D%5Cleft(7%7B%2C%7D4%5Cright)" alt="B=\left(7{,}4\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Cfrac%7B-5%2B7%7D%7B2%7D%7B%2C%7D%5C%20%5Cfrac%7B1%2B4%7D%7B2%7D%5Cright)%3D%5Cleft(1%7B%2C%7D%5C%202%5Cfrac%7B1%7D%7B2%7D%5Cright)" alt="\left(\frac{-5+7}{2}{,}\ \frac{1+4}{2}\right)=\left(1{,}\ 2\frac{1}{2}\right)"/></div> 2019-05-03T09:29:51+03:00