Given Vector A with magintude 9.17 feet and Vector B with magnitude of 10.58 feet, what is the resultant of the two vectors added together?
Asn: Do we just add to the values together? 19.75 ft???
To find the resultant of two vectors added together, we need to consider both the magnitudes and the directions of the vectors.
To add two vectors, we can construct a parallelogram with the two vectors as adjacent sides, and the diagonal of the parallelogram represents the resultant vector. The magnitude of the resultant vector can be found using the Law of Cosines.
Let's calculate the resultant vector using the given magnitudes of Vector A and Vector B.
Magnitude of Vector A = 9.17 feet
Magnitude of Vector B = 10.58 feet
To find the resultant, we need to use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(theta)
Where:
- c is the magnitude of the resultant vector
- a and b are the magnitudes of the individual vectors
- theta is the angle between the two vectors
As the problem does not provide the angle between the vectors, we assume that the two vectors are colinear (have the same direction and angle is 0 degrees). In this case, the formula simplifies to:
c = sqrt(a^2 + b^2)
Substituting the given values:
c = sqrt((9.17 feet)^2 + (10.58 feet)^2)
c = sqrt(84.0689 feet^2 + 111.8564 feet^2)
c = sqrt(195.9253 feet^2)
c ≈ 13.98 feet
Therefore, the magnitude of the resultant vector is approximately 13.98 feet.