Subjects algebra

Vektoru Operacijas

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1. Uzdevums: Aprēķināt vektoru operācijas ar dotajiem vektoriem $\vec{a} = (3; 3)$ un $\vec{b} = (-6; -6)$.\n\n2. Formulas un noteikumi:\n- Vektoru summa: $\vec{a} + \vec{b} = (a_x + b_x; a_y + b_y)$\n- Vektoru starpība: $\vec{a} - \vec{b} = (a_x - b_x; a_y - b_y)$\n- Skaitļa reizinājums ar vektoru: $k \vec{a} = (k a_x; k a_y)$\n- Pusējs vektors: $\frac{1}{2} \vec{b} = \left(\frac{b_x}{2}; \frac{b_y}{2}\right)$\n\n3. Aprēķini:\n- $\vec{a} + \vec{b} = (3 + (-6); 3 + (-6)) = (-3; -3)$\n- $\vec{a} - \vec{b} = (3 - (-6); 3 - (-6)) = (9; 9)$\n- $-5 \vec{a} = (-5 \times 3; -5 \times 3) = (-15; -15)$\n- $\frac{1}{2} \vec{b} = \left(\frac{-6}{2}; \frac{-6}{2}\right) = (-3; -3)$\n\n4. Atbildes:\n1) $\vec{a} + \vec{b} = (-3; -3)$\n2) $\vec{a} - \vec{b} = (9; 9)$\n3) $-5 \vec{a} = (-15; -15)$\n4) $\frac{1}{2} \vec{b} = (-3; -3)$