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 4 Modifying above upper R upper S with right arrow.
(1 point)
Responses
left angle bracket 18 comma 19 right angle bracket
Image with alt text: left angle bracket 18 comma 19 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 negative 14 comma negative 21 right angle bracket
Image with alt text: left angle bracket negative 14 comma negative 21 right angle bracket
left angle bracket negative 18 comma negative 19 right angle bracket
To find the component form of the vector PQ + 4RS, we first calculate PQ and 4RS separately:
PQ = Q - P = (7, 3) - (5, 4) = (2, -1)
RS = S - R = (4, 1) - (8, 6) = (-4, -5)
Now we find the sum of PQ and 4RS:
PQ + 4RS = (2, -1) + 4(-4, -5) = (2, -1) + (-16, -20) = (2 - 16, -1 - 20) = (-14, -21)
Therefore, the component form of the vector PQ + 4RS is < -14, -21 >.