Question

• Find the area of ​​a triangle constructed on vectors а‾ = ı‾ + ȷ‾ , ̅b‾=2ȷ‾.

Answer 1

$$\vec{a}\times\vec{b}=\begin{vmatrix} \vec{i} & \vec{j}& \vec{k} \\ 1 & 1 & 0 \\ 0 & 2 & 0 \\ \end{vmatrix}=\vec{k}(2-0)=2\vec{k}$$ $$Area=A=\dfrac{1}{2}|\vec{a}\times\vec{b}|=\dfrac{1}{2}(2)=1({units}^2)$$

1 square unit.