Project ID:
7200020189
Accepted:
Type:
Layout:
Question:
In the parallelogram $ABCD$, denote the vector $\vec{AB}$ as $\vec{u}$ and the vector $\vec{AD}$ as $\vec{v}$. Match the pairs of vectors $\vec{u}$ and $\vec{v}$ with the area of the corresponding parallelogram $ABCD$.
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Hint: It can be shown that the area of the parallelogram $ABCD$, where $\vec{AB}=\vec{u}=(u_1, u_2)$ and $\vec{AD}= \vec{v}= (v_1, v_2)$, is equal to the absolute value of the determinant $\begin{vmatrix} u_1 & u_2 \\ v_1 & v_2 \end{vmatrix}$.
Questions Title:
Vectors
Answers Title:
Areas
Question 1:
$\vec{u}= (1 ; 2)$, $\vec{v}= (2 ; 6)$
Answer 1:
$S = 2$
Question 2:
$\vec{u}= (2 ; 0)$, $\vec{v}= (0 ; 2)$
Answer 2:
$S = 4$
Question 3:
$\vec{u}= (1 ; 3)$, $\vec{v}= (-6 ; 2)$
Answer 3:
$S = 20$
Question 4:
$\vec{u}= (3 ; 5)$, $\vec{v}= (1 ; 5)$
Answer 4:
$S = 10$
Question 5:
$\vec{u}= (1 ; 1)$, $\vec{v}= (-2 ; 3)$
Answer 5:
$S = 5$
Question 6:
$\vec{u}= (0 ; 3)$, $\vec{v}= (-3 ; 3)$
Answer 6:
$S = 9$