Question

vectors b and c are shown in the coordinate plane.Vector f is given by f = b + cWhat is the approximate magnitude of vector ?8.016191310

Answer 1

When two vectors are added, the maximum magnitude of their sum can be reached when they point in the same direction, and the minimum magnitude of their sum is reached when they point towards opposite directions.

Since the magnitude of vector B is 5.6 and the magnitude of vector C is 4.8, then, the maximum and minimum magnitudes that the sum B+C can have are:

`\begin{gathered} |B+C|_(max)=5.6+4.8=10.4 \\ |B+C|_(min)=5.6-4.8=0.8 \end{gathered}`

From the given options, only 8.0 and 10 can be the magnitude of the vector F, which is equal to B+C.

To find the magnitude of F analitically, find the vertical and horizontal components of B and C. Add them to find the vertical and horizontal components of F and use the Pythagorean Theorem to find the magnitude of F:

`\begin{gathered} B_x=-5.6\cos(33º)\approx-4.7 \\ B_y=-5.6\sin(33º)\approx-3.0 \\ \\ C_x=4.8\sin(22º)\approx1.8 \\ C_y=-4.8\cos(22º)\approx-4.45 \\ \end{gathered}`

Then:

`\begin{gathered} F_x\approx-4.7+1.8=-2.9 \\ F_y\approx-3.0-4.45=-7.45 \\ \\ \Rightarrow|F|=√((-2.9)^2+(-7.45)^2)\approx8.0 \end{gathered}`

Therefore, the correct choice is: 8.0.