Two displacement vectors of magnitudes 21 cm and 79 cm are added. Which one of the following is the only possible choice for the magnitude of the resultant?
A)0 cm
B)28 cm
C)37 cm
D)82 cm
E)114 cm

Question

Quizplus · Accepted Answer

In order to find the magnitude of the resultant of two vectors, we need to use the Pythagorean theorem. The magnitude of the resultant is the square root of the sum of the squares of the magnitudes of the two vectors.

Let's call the vectors A and B, where |A| = 21 cm and |B| = 79 cm. Then,

|A + B| = √(|A|² + |B|²) 
|A + B| = √(21² + 79²) 
|A + B| = √(6722)

Using a calculator or estimation, we can see that the only possible choice for the magnitude of the resultant is 82 cm (choice D).

Two Displacement Vectors of Magnitudes 21 Cm and 79 Cm