Use the information from part A to find the magnitude of the vector Modifying above upper P upper Q with right arrow plus 5 Modifying above upper R upper S with right arrow.
(1 point)
Responses
1,000
1,000
10 start root 10 end root
Image with alt text: 10 start root 10 end root
2 start root 11 end root
Image with alt text: 2 start root 11 end root
2 start root 10 end root
To find the magnitude of the vector PQ + 5RS, we first need to find the vectors PQ and RS separately.
Given that PQ = 5i + 5j and RS = 4i + 3j, we can calculate the combined vector PQ + 5RS as follows:
PQ + 5RS = (5i + 5j) + 5(4i + 3j)
= 5i + 5j + 20i + 15j
= 25i + 20j
Now, to find the magnitude of the vector PQ + 5RS, we use the formula:
|PQ + 5RS| = sqrt((25)^2 + (20)^2)
= sqrt(625 + 400)
= sqrt(1025)
= 5√41
Therefore, the magnitude of the vector PQ + 5RS is 5√41.