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

Question 1 of 5

Question

scalar $c$

{"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":"Correct!","type":"correct","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":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"107,145,140,178\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"253,147,294,180\"}]"}

Question

$x$ component of the vector $\boldsymbol{\vec{E} = c\vec{A}}$

{"title":"x component of the vector E = cA","description":"Correct!","type":"correct","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":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"107,145,140,178\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"253,147,294,180\"}]"}

Question

$y$ component of the vector $\boldsymbol{\vec{E} = c\vec{A}}$

{"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":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"107,145,140,178\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"253,147,294,180\"}]"}

Question

$y$ component of the vector $\boldsymbol{\vec{A}}$

{"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\"}]"}

Question

$x$ component of the vector $\boldsymbol{\vec{A}}$

{"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":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"256,29,285,65\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"y component of the vector E = cA","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"107,145,140,178\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","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.