Given that upper P equals left parenthesis 5 comma 4 right parenthesis, upper Q equals left parenthesis 7 comma 3 right parenthesis, upper R equals left parenthesis 8 comma 6 right parenthesis, and upper S equals left parenthesis 4 comma 1 right parenthesis, find the component form of the vector Modifying above upper P upper Q with right arrow plus 3 Modifying above upper R upper S with right arrow.
(1 point)
Responses
left angle bracket negative 10 comma negative 16 right angle bracket
Image with alt text: left angle bracket negative 10 comma negative 16 right angle bracket
left angle bracket negative 6 comma negative 4 right angle bracket
Image with alt text: left angle bracket negative 6 comma negative 4 right angle bracket
left angle bracket negative 2 comma negative 6 right angle bracket
Image with alt text: left angle bracket negative 2 comma negative 6 right angle bracket
left-angle-bracket 14 comma 14 right-angle-bracket
To find the component form of the vector Modifying above upper P upper Q with right arrow plus 3 Modifying above upper R upper S with right arrow, we first calculate the vector Modifying above upper P upper Q: (7-5, 3-4) = (2, -1). Then we calculate 3 times the vector Modifying above upper R upper S: 3(8-4, 6-1) = 3(4, 5) = (12, 15).
Adding the two calculated vectors together: (2+12, -1+15) = (14, 14).
Therefore, the component form of the vector is left angle bracket 14, 14 right angle bracket.