Teorem 1. Vektorun ox üzrə proyeksiyası onun uzunluğu ilə vektor və onun müsbət istiqaməti arasındakı bucağın kosinusu hasilinə bərabərdir.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA04AAAILAQMAAADljF6pAAAACXBIWXMAAC4kAAAuIwFloA/OAAAABlBMVEUAAAD///+l2Z/dAAANeElEQVR4nO3dy+7dRhkA8Dk5VcwCYbFEKjVvQCU2LCq5b8IC3oGsalcsskHK67DDFRIskIh4AJQpEXSZQV0wVdxxZ+b4Nr7MN+P5/CmJ7MU///+5/WKfb+4Xs47qaNlFXdRFXdRFXdRFXdRFXdRFXdRFXdRFffBUW5FRoiCjWE5FKZZRUZLdqSjBblQUp6Nqhpjs3hmKMVZ9gFRGR+U1GVXSURUVpSipjiosFFNUSbglpG6SjhJUOXt741RFo7zVVJRgZAX+B0tRRSBnZAU+pyuFG02VHyRV0FA1e0pHVQ0RpVNVkxNRWSdoKKW/KDJK5014zcZ3hGp1XssJqZyEkrqwIgp2Q9U0lNCUyZgUAZXpICw1VVBQ0hYi31BQgqgU1lRNRPGspaoxiUxQ1QNNhYmok46jVi1AqqSj8CSIQowKiCqIKIF6/QAqJ6NKTMlfNFZkFPJxURd1URd1URd1DiXoKMQOJohCbAiDFGLjAKIQW1dQzxlimxGkSv3zexqqMP+U351P1Y9G42uc9ghAWQTpCgIUZggCFGYIQlRJRxV0VE5HUc1jqukGAGu6AUBGNwDI6IbK2FOyoTKWY4YgQDWIXxZAccRc0E8VAjEuAEoixgVAtYi5IEApxBAEqA4xF4QoxMmIfqo0Y+vVh0cJvGj3U1Un8coRiGrxxkUgSuGVWRBloh0pwwCpBu0KgpQZgyFoiRhKEFFdZ6Od6Kwk3XclaSLQTLpVNOmKkvpNhzjRHDyrjuasGkOhNR3fFYpbjyTYv+0pgiRsD47VdAyicIr8MKqio0oaSmDltzCFVoqEUShlYwj1KU60h1ASJ9phqr21ONEeQN07nGiHKWWmgxUkVFfoVJzTUCbDwIj2IApnPk4QJVHiIohSdFSHUr0IpXIqqsHI28MolGgPo1AW84ZRKHl7GKUw8nYv1Y6/YUS7l5rmt9UIIeifLlBOVHoIBlIYi7z9LZGREghxEXhWGHl74Fm1CCEYSCmEDNd/AYvxV4RoD6UQ8vZQCmFmeziVnLBCKZmesEIphJpMKIWQt/vT1ezT00MwmEqvXgRT6SEYTKVXL4Kplo5Kr8kEU+nRHk7VqcVIYHnVISSscCo5YYVTyQkrnEpOWOFUcp9MOJVckwkP9i61WzCCahJDMIJKDcEIKjUEI6g2sXoRQanEDDeCSu0oiaOSoj2GSpywGkPxtBCMoRIr0zFUYrTHUInRHkMlRnvUMoe0mkwUlZa3R1Fp0R5FpfXJRIVFWp9MFJUW7f4LWC4eSIr2qLNK65OJO6ukHsjweqB9YKsYWb4Ih9ocXXpxCrVZmX6OQYnV525F+1fnUFsZrvglBrV6ZLM99zcEql09spnhvkWg1sdm9SJws5dIarN6odY6AuVmuP13qX5/EjXLBVfpDpNyZoKruCIllppXptuR+vMZ1DzaxblnNa9eNHEF5QGqHH6PLJNjqdmQT2xHRiw1+/zY1Rax1CzaT6emaI9drhJNTQuKTqemaI9dlhBNTedyOtXSUVPvhbjXJ1NjDZff43aRi6eaIdp5Hrc3Xjw1rmnjxdnUGA2aKs6l2lOo/209OGa4vESk+OajQ7Q3mFSz+egQ7bhUtflon+FqqjyZGqKdgBoy3KY6nWr7uNBUcTI1lPm1S/0/jdp5+JELLqhvk6h6+2E+UIiFyA7Vl/n1s7jOrSNU34EWu4DkCNVnuLELBY5QfYaLS1Xbjz8SVuxOkEfOqq/hklCPDBeV2nvukeGSUI/2HGN1iUbtXUAb7YrdV72gCVS1S+Vm1924/Zr8F3CHstGubuu+3RMoE+3I1N4TpvdC3UnOyoQgEWVCkIgyGS4RZUYsNMV3n0ekdPVCZTsVbXSKaWqz+YBNmWiPHfQ5SJme6ZeY1P6th47MmT5IHZlpdJDaGJ8D7+F3lFqPRoMlylFqNTjSgl/ewQhcjs9x/UH5SdRiHKbRHwSls6PUYhymqeDbBSZQxezPWlPQHJ1jpfBqjL2u4KV7R6nFqGMytVcPNIc7SlGX8ASJo9/VYm7sg/JbhynhUE2Velae5+T6ApY0VMAuW4fDQrhJuBB3qF3ipb70U68cKjuRqmZxYaikC/gXH3XvZjlRMuU7ZDaPmlMpkc+TnaaenEoVMwqeTpVCzTb5bXJ4SmQK1UwhyPPEjAmipnLXUsA7jlNFx6do5xk8WTvlrMT0Xp4lFvheqtA5bjX+lSVWY0CqHP+6i7TKGUDNpnbI27nU7P7XIXtRpYRFN90Osz2basagawM6B49TmWmOVP1f6lQqdwr9gO7pJGrWpgrYnDmRyoc/G3gGfxLVTWkpYHWWl/KNE8mim0d7wCLfw9UYWeofzSxhpVG+WZqW4tO7mzTKVw+0mxzMbj8s0ihfRfrh0VGzd8N3W0yjui1qbyg1kZpewc+mpuFc+B6SidR/sKiYTOu9oaJuRT5FYHk2NZ1VhU21hft3Wm7hpWT++Hfo1pfnUcPNbIfNDs6khvl0T3oqqcAPo/qqTOtQW5kTAvWYv6KcC7h1j1EUyt6XNZ8/e9pZsfuyanDKWZk2yLpqe8pZtQ9qEX+nUOpBLZo8p1BdT7kp+PWZlNvmOYeq2ca3dS7lfFtbVfDk7NZuCm6PeTG8tSYr/axsGs6VGxjnUPJx8dzurBenUI803Lk7auaYlMzGVz1CnUNN/HSq61PwNJzwKp7yD1QMH9xHu341UOQjULzP2hugyD9eORsp0X9ZwvfyFGo6dLRz82W1QH8MAtXae4EwcOWXlwrbIsHch90OqAI318Oos5sLZ3pjgJvreSMwcOMHO3ClCxGg6wKDsrOyOeuE//UYlO0tEaxsj1OBYdF75vY3odSqmyeKMn2D/t7HkRJfrF8Ys2Zc6VJ4OT0736b4p+vE7j2red3ZdBzqUF+s8VFu8I9Us+7n9V/A+RfzdWdWE3WLhTftDrUxjzuc4p1tyy26tFr3CzhMOeFmZu9Jtmykeqj8OFWaT6oWCWspD+9g671uAKqaUbnNdcOpZWxHUHbS+TIN41GzP2zuZ6hq/hK5E4Hr5pifcnI0W9br4spNL6dQdiiwyTp3HsQy9h3KbUAoX8bkUHYcRqdhdzbdMkVP1Oe3xbUOp5RJKOK+3Ndrm9K5pbjJRSoOpuw4jMkunA/fpQozCuo8CZxVNfvLjMPo7ML9dubberpUe+NuKo6hbo/sQr9j+ogdStcX5W0xazKCauxduUpNqSmQV9s5zajanV3grSu4FLeLEUzO1E5ZwS5VWWr+bS2jxDmUk1ztt2y+A0MN/8PF+rYZJe62+fIjVr4Z3u8ZLHerzbZ5alrEj0bkYxR3h5IjtTh++91b26y5/eNXzhvdiWDCXDaWKXuDwqHDZDHdfTqrbptyDt0ifPHPri1U37N0Y2aMtn3bt7HMLSbk+FIPxWEKOn4x/aqv4GJV33QBMajZkfuohooyDQmOSGWrec8DJQzVsOyN/l396WdmM5ivxUnU3Z5V0S2PV8/rXP63et11f2W/Xn3gx39v/vVVvUd1PqpcUYvjj+Xvft6p7ttn5uOGHKiWOuE/+bdD5au+iIHiD8o9Ze/Ruv8t8zky50O6MqNYiyx0pHTlPgOafd7j5ePjsnY63Vvn3MZ8oEwd5A4PocCHPavC/KZrQWKXav1N9HCqstRiJc5I5aZ+UOBQj+u3TymcmzTJ4fp5qRyDmqbv69LfKbEGqsai1Fhp2KOiz+r1Xi3xy6r/Re6eFbzQY360N8mAl8hFbXeiJJwrzQ7OwKxF1yGcOvxAmds+x1AmiwVeL5jbvO4pHelN1OaKDKb4HnWP2zKSMXDqHGduS36k1i05X+bbBlBNBMU2h6EwqNWCKvbF7jWVgdQ8r5tR+eKltS7gq12qBql6n1q+0xdk8t6AEcj2qcU7vXcWllkAdZd7VOW+svVRbdGAMyrNQNMGZbv/3UP6U2nDfuqXbE//FrVePCj8QdZAKd72TLzcpJafKpjwUTVU5Vn1T4/l1erKm8ncPgrqQ151G83q7Esq4+zzcp8Cz2r5fxk7VVZ1GKGLFc/GMOA8W7X8xP3RA1nwm48CO+FzkKoGquT39R6gEdTy2KfsMon9N2JQ0+Gbh6dwKd/eYtQUJ6JuHeKSfzsiuhOEmlLlzs5GR6mdxXa61JEFtBAvliq2nvrGrtZApIyynePWnxkqqj4Mn9V2+8R2VYAL8eKondXhlnqKQb2xP7Xy3Ef9JG4LdYC6yz3qVrNPMKiXPaUW9avxaJiuCH6GQdlnPmFZ66FMHw8SpWsWmbztUJzp6gA0QyWY0s2jO7/JjzZzcKFbmXeOQVVdP5HnJn+8SeloMXUPBKobqLv8eJNqWaHrHriUerZJmfGPEpfK96ZZmxkTAjEC7USo7QqG2VIcLdj7lohnVYtCS8I6O2WrAcOTqNwkX8/mpWiULhRNKeKpy0Qtg/BSjd2K0NPuwTsrO6zm29cbk+pMwVRSUb6WNy7lvfMfOuV7EpPyLlfEprI/kFEf7TevsSnPl6XwarcQBUzSe18pzy5U8ZTyUnitRnOsO6pnB16z+0F5Oi/AjXujKHDuPR4FDh3hUfsDCPgU3nFRF3VR7yn1PR3VXdTJVEVHYR8XdVEXdVEX9cFRPwAQCYiz0vCIngAAAABJRU5ErkJggg==)
İsbatı. Tutaq ki, vektoru oxu ilə bucağı əmələ gətirir. Əgər bucağı bucağı iti bucaqdırsa onda -dən ![](data:image/png;base64,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)
Əgər bucağı kordursa, onda vektorunun üzrə proyeksiyası mənfidir.
olduğundan onun bu ox üzrə proyeksiyası sıfra bərabərdir;
Əgər və onların istiqamətləri əks işarəlidirsə ![](data:image/png;base64,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)
Beləliklə istənilən halda
Teorem 2. İki vektorun cəminin ox üzrə proyeksiyası bu vektorların proyeksiyaları cəminə bərabərdir.
Dostları ilə paylaş: |