\(9 \) Given vectors \( u = ( 1,0 , - 1 ) , v = ( 2,1,3 ) \) and \( w = ( c , 1,2 ) \) .
i) Find \( c \) if \( u \) is orthogonal to \( w \) .
ii) Find a unit vector in the direction of \( ( u + v ) \) .
Pregunta
Answer
i) \(u\cdot w= c- 2= 0\Rightarrow c= 2\)
ii)
\(u+ v= (3,1,2)\\(3,1,2)\cdot \frac{1}{\sqrt{3^{2}+ 1^{2}+ 2^{2} } } = (\frac{3}{\sqrt{14} } ,\frac{1}{\sqrt{14}} ,\frac{2}{\sqrt{14}} )\)
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