Take Note Property: Adding Vectors

For a ⇀ = 〈 x 1 , y 1 〉 and c ⇀ = 〈 x 2 , y 2 〉 , modified a with right harpoon up above , equals left pointing angle bracket , x sub 1 , comma , y sub 1 , right pointing angle bracket and , modified c with right harpoon up above , equals left pointing angle bracket , x sub 2 , comma , y sub 2 , right pointing angle bracket comma

a ⇀ + c ⇀ = 〈 x 1 + x 2 , y 1 + y 2 〉 modified a with right harpoon up above , plus , modified c with right harpoon up above , equals left pointing angle bracket , x sub 1 , plus , x sub 2 , comma , y sub 1 , plus , y sub 2 , right pointing angle bracket

Problem 4 Adding Vectors

Vectors a ⇀ modified a with right harpoon up above and c ⇀ modified c with right harpoon up above are shown below. a ⇀ = 〈 − 4 , − 3 〉 modified a with right harpoon up above , equals left pointing angle bracket negative 4 comma negative 3 right pointing angle bracket and c ⇀ = 〈 1 , − 2 〉 . modified c with right harpoon up above , equals left pointing angle bracket 1 comma negative 2 right pointing angle bracket . What is the resultant e ⇀ modified e with right harpoon up above of the two vectors as an ordered pair? Draw e ⇀ . modified e with right harpoon up above , .

e ⇀ = a ⇀ + c ⇀     = 〈 − 4 , − 3 〉 + 〈 1 , − 2 〉     = 〈 − 4 + 1 , − 3 + ( − 2 ) 〉 Add the coordinates .   = 〈 − 3 , − 5 〉 Simplify . table with 4 rows and 3 columns , row1 column 1 , modified e with right harpoon up above , column 2 equals , modified a with right harpoon up above , plus , modified c with right harpoon up above , column 3 , row2 column 1 , , column 2 equals left pointing angle bracket negative 4 comma negative 3 right pointing angle bracket plus left pointing angle bracket 1 comma negative 2 right pointing angle bracket , column 3 , row3 column 1 , , column 2 equals left pointing angle bracket negative 4 plus 1 comma negative 3 plus . open , negative 2 , close . right pointing angle bracket , column 3 cap addthecoordinates . . , row4 column 1 , , column 2 equals left pointing angle bracket negative 3 comma negative 5 right pointing angle bracket , column 3 cap simplify , . , end table

〈 − 3 , − 5 〉 left pointing angle bracket negative 3 comma negative 5 right pointing angle bracket is the resultant.

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✓ Got It?

4. What is the resultant of 〈 2 , 3 〉  and  〈 − 4 , − 2 〉 left pointing angle bracket 2 comma , 3 right pointing angle bracket , and , left pointing angle bracket negative 4 comma negative 2 right pointing angle bracket as an ordered pair?