Rules for multiplying a vector by a scalar using components (3-5)

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Question 1 of 5

Question

\(y\) component of the vector \(\boldsymbol{\vec{A}}\)
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{"title":"x component of the vector E = cA","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"103,35,134,70\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"scalar c","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"193,19,219,57\"},{\"shape\":\"rect\",\"coords\":\"186,131,222,162\"}]"} {"title":"x component of the vector A","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"256,29,285,65\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"y component of the vector E = cA","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"107,145,140,178\"}]"} {"title":"y component of the vector A","description":"Correct!","type":"correct","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"253,147,294,180\"}]"}

Review

Multiplying a vector \(\boldsymbol{\vec{A}}\) by a scalar \(c\) gives a new vector \(\boldsymbol{\vec{E} = c\vec{A}}\) whose components are just the components of \(\boldsymbol{\vec{A}}\) multiplied by \(c\). Note that if \(c\) is negative, the sign of each vector component is reversed—which means that the direction of the vector as a whole is reversed.