The answer is letter d, 8.3.
Here’s a solution for the given problem:
We have:
B = 6i - 8j
Let A be unknown; we'll denote A as = mi + nj
The resultant A+B lies along the x-axis (which implies A+B = Ki + 0j, where K is yet to be determined,
and we also know the magnitude of A+B is equivalent to the magnitude of A,
therefore, mag(A+B)=K=sqrt(m^2+n^2), or K^2 = m^2+n^2.
Using vector addition, A+B becomes (m+6)i + (n-8)j.
Since we know A+B = Ki + 0j, we can establish that:
m + 6 = K
n - 8 = 0, which gives n=8.
Thus, K^2=m^2+n^2 means (m+6)^2 = m^2 +8^2
= m^2 + 12m + 36 = m^2 + 64
which gives us 12m = 28
m = 2.33333...
Consequently, the magnitude of A is sqrt[(2.333...)^2 + 8^2] = 8.3333.
