iran-konkur 2023 Q35

iran-konkur · Other · konkur-riazi_1402_general Vectors Introduction & 2D Area Computation Using Vectors
35. Suppose $\vec{a}$ and $\vec{b}$ are non-zero vectors whose dot product is $-\dfrac{3}{5}$ times the product of their magnitudes. What is the area of the triangle formed by the vectors $\left(\dfrac{3\vec{a}}{|\vec{a}|}+\dfrac{2\vec{b}}{|\vec{b}|}\right)$ and $\left(\dfrac{\vec{a}}{|\vec{a}|}-\dfrac{2\vec{b}}{|\vec{b}|}\right)$?
(1) $6/4$ (2) $4/8$ (3) $3/2$ (4) $1/6$
\textbf{35.} Suppose $\vec{a}$ and $\vec{b}$ are non-zero vectors whose dot product is $-\dfrac{3}{5}$ times the product of their magnitudes. What is the area of the triangle formed by the vectors $\left(\dfrac{3\vec{a}}{|\vec{a}|}+\dfrac{2\vec{b}}{|\vec{b}|}\right)$ and $\left(\dfrac{\vec{a}}{|\vec{a}|}-\dfrac{2\vec{b}}{|\vec{b}|}\right)$?

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(1) $6/4$ \hspace{1cm} (2) $4/8$ \hspace{1cm} (3) $3/2$ \hspace{1cm} (4) $1/6$
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