Vector A, which is directed along an x axis, is to be added to vector , which has a magnitude of 8.0 m. The su

Question

Vector A, which is directed along an x axis, is to be added to vector b, which has a magnitude of 8.0 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 7 times that of A. What is the magnitude of A? (Enter your answer to 4 significant figures.)

Answer 1

Let the sum of vectors a and b to be c. That is:
a + b = c
or a + b + (-c) = 0
Since a is "directed along an x axis", c is "is directed along the y axis", we are dealing with a right triangle with a and -c to be two legs. Since:
|-c| = |c| = 7|a|, we have:
64 = |b|^2 = |a|^2 + |-c|^2 = 50 |a|^2
Therefore the magnitude of a: |a| = sqrt(64/50) = 1.13137085
... ≈ 1.131 (m)