Rules for vector subtraction using components (3-4)

Question 1 of 6

Question

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

{"title":"x component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"84,21,113,52\"}]"} {"title":"x component of the vector A","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"183,27,213,53\"}]"} {"title":"x component of the vector B","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"272,28,301,52\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"y component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"75,111,120,144\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"178,105,212,139\"}]"} {"title":"y component of the vector B","description":"Correct!","type":"correct","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"259,112,300,137\"}]"}

Question

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

{"title":"x component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"86,26,117,53\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"x component of the vector A","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"185,26,213,54\"}]"} {"title":"x component of the vector B","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"278,28,302,56\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"y component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"75,111,120,144\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"178,105,212,139\"}]"} {"title":"y component of the vector B","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"259,112,300,137\"}]"}

Question

$y$ component of the vector $\boldsymbol{\vec{D} = \vec{A} - \vec{B}}$

{"title":"x component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"93,23,114,55\"}]"} {"title":"x component of the vector A","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"180,25,211,52\"}]"} {"title":"x component of the vector B","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"poly\",\"coords\":\"113,132\"},{\"shape\":\"rect\",\"coords\":\"279,26,301,53\"}]"} {"title":"y component of the vector D = A - B","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"75,111,120,144\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"178,105,212,139\"}]"} {"title":"y component of the vector B","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"259,112,300,137\"}]"}

Question

$x$ component of the vector $\boldsymbol{\vec{D} = \vec{A} - \vec{B}}$

{"title":"x component of the vector D = A - B","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"85,26,114,56\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"x component of the vector A","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"178,32,214,52\"}]"} {"title":"x component of the vector B","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,26,301,52\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"y component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"75,111,120,144\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"178,105,212,139\"}]"} {"title":"y component of the vector B","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"259,112,300,137\"}]"}

Question

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

{"title":"x component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"91,27,111,51\"},{\"shape\":\"poly\",\"coords\":\"82,133\"}]"} {"title":"x component of the vector A","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"183,24,207,55\"}]"} {"title":"x component of the vector B","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"272,28,301,51\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"y component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"75,111,120,144\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"178,105,212,139\"}]"} {"title":"y component of the vector B","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"259,112,300,137\"}]"}

Question

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

{"title":"x component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"84,28,113,55\"}]"} {"title":"x component of the vector A","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"182,23,210,53\"}]"} {"title":"x component of the vector B","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"279,24,300,49\"},{\"shape\":\"poly\",\"coords\":\"113,132\"}]"} {"title":"y component of the vector D = A - B","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"75,111,120,144\"}]"} {"title":"y component of the vector A","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"178,105,212,139\"}]"} {"title":"y component of the vector B","description":"Incorrect","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"259,112,300,137\"}]"}

Review

If we subtract $\boldsymbol{\vec{B}}$ from $\boldsymbol{\vec{A}}$ to form the vector difference $\boldsymbol{\vec{D} = \vec{A} - \vec{B} = \vec{A} + (- \vec{B})}$ , each component of $\boldsymbol{\vec{D}}$ is equal to the sum of the corresponding components of $\boldsymbol{\vec{A}}$ and $\boldsymbol{-\vec{B}}$ . The components of $\boldsymbol{-\vec{B}}$ are $-\vec{B}_x$ and $-\vec{B}_y$ , so the components of $\boldsymbol{\vec{D}}$ are $\vec{D}_x = A_x + (-B_x) = A_x - B_x$ and $D_y = A_y + (-B_y) = A_y - B_y$ .