Q2: $$ (8 $$ Marks) For the points, $$ P(0,1,-1), Q(1,2,0) $$, and $$ R(1,3,2) $$ : A- If $$ u=\overline{P Q} $$ and $$ v=\overline{P R} $$, find the vector projection of $$ u $$ onto $$ v $$, and the scalar component of $$ u $$ in the direction of $$ v $$. B. Find the area of the triangle with vertices $$ P, Q $$, and $$ R $$.

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Mann Conner · Accepted Answer

**الإجابة:** أ. الإسقاط المتّجه لـ $$ \mathbf{u} $$ على $$ \mathbf{v} $$ هو $$ \left( \frac{3}{7}, \ \frac{6}{7}, \ \frac{9}{7} \right) $$ والمكون السلمي لـ $$ \mathbf{u} $$ في اتجاه $$ \mathbf{v} $$ هو $$ \frac{6}{\sqrt{14}} $$. ب. مساحة المثلث ذو الرؤوس $$ P, Q $$ و $$ R $$ هي $$ \frac{\sqrt{6}}{2} $$.

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