Avector a is added to b=6i-8j. the resultant vector is in the positive x direction and has a magnitude equal to a . what is the magnitude of a? a)11 b)7.1 c)5.1 d)8.3 e)12.2

The correct answer would be letter d, 8.3.

Solution for the problem follows:

Given are:

B = 6i - 8j 

A is unknown; let A be = mi + nj 

A+B is along the x axis (therefore A+B = Ki + 0j, where K is unknown,

but then again the magnitude of A+B is the similar as the magnitude of A,

so mag(A+B)=K=sqrt(m^2+n^2), or K^2 = m^2+n^2. 

A+B, from simple vector addition, will be now (m+6)i + (n-8)j.

Ever since we previously know A+B = Ki + 0j, we now know that: 

m+6 = K 

n-8 = 0, which implies n=8. 

Thus, K^2=m^2+n^2 > (m+6)^2 = m^2 +8^2 

= m^2 + 12m + 36 = m^2 + 64 

= 12m = 28 

= m = 2.33333... 

Therefore, the magnitude of A is sqrt[(2.333...)^2 + 8^2] = 8.3333

they start with the same

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.