Find the vector v with the magnitude $\frac { 15 } { 2 } \text { and direction of } \mathbf { u } = \{ 18 , - 18,9 \}$
A) $\mathbf { v } = \left( 5 , - 5 , \frac { 5 } { 2 } \right)$
B) $\mathbf { v } = ( 5 , - 5,5 )$
C) $\mathbf { v } = \left( 9 , - 9 , \frac { 9 } { 2 } \right\}$
D) $\mathbf { v } = \left( \frac { 5 } { 2 } , - \frac { 5 } { 2 } , \frac { 5 } { 18 } \right)$
E) $\mathbf { v } = \left( \frac { 5 } { 18 } , - \frac { 5 } { 18 } , \frac { 5 } { 6 } \right)$

Question

Find the vector v with the magnitude $\frac { 15 } { 2 } \text { and direction of } \mathbf { u } = \{ 18 , - 18,9 \}$ 
A) $\mathbf { v } = \left( 5 , - 5 , \frac { 5 } { 2 } \right)$
B) $\mathbf { v } = ( 5 , - 5,5 )$
C) $\mathbf { v } = \left( 9 , - 9 , \frac { 9 } { 2 } \right\}$
D) $\mathbf { v } = \left( \frac { 5 } { 2 } , - \frac { 5 } { 2 } , \frac { 5 } { 18 } \right)$
E) $\mathbf { v } = \left( \frac { 5 } { 18 } , - \frac { 5 } { 18 } , \frac { 5 } { 6 } \right)$

Quizplus · Accepted Answer

To find the vector $ \mathbf{v} $ with the same direction as $ \mathbf{u} = \{ 18, -18, 9 \} $ but with a magnitude of $ \frac{15}{2} $, we first normalize $ \mathbf{u} $ and then scale it by $ \frac{15}{2} $. The magnitude of $ \mathbf{u} $ is $ \sqrt{18^2 + (-18)^2 + 9^2} = \sqrt{324 + 324 + 81} = \sqrt{729} = 27 $. The normalized vector of $ \mathbf{u} $ is $ \frac{1}{27} \mathbf{u} = \left( \frac{2}{3}, -\frac{2}{3}, \frac{1}{3} \right) $. Scaling this by $ \frac{15}{2} $ gives $ \mathbf{v} = \left( 5, -5, \frac{5}{2} \right) $.

Find the Vector V with the Magnitude 152 and direction of u={18,−18,9}\frac { 15 } { 2 } \text { and direction of } \mathbf { u } = \{ 18 , - 18,9 \}215​ and direction of u={18,−18,9}

Find the Vector V with the Magnitude $\frac { 15 } { 2 } \text { and direction of } \mathbf { u } = \{ 18 , - 18,9 \}$