The magnitudes of two displacement vectors are A = 20 m and B = 6 m. What are the largest and the smallest values of the magnitude of the resultant R⃗ =A⃗ +B⃗ ?

The largest value is 26 m. The smallest value is 14 m. The magnitude of the resultant vector is 20.88 m.

The magnitude of two displacement vectors refers to the change in the distance the vectors have covered.

From the parameters given:

The largest values = A + B

= 20 m + 6 m

= 26 m

The smallest values = A - B

= 20 m - 6 m

= 14 m

The resultant vector R of the magnitude is:

R = 20.88 m

Learn more about the magnitude of two vectors here:

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R = 26 m and R = 14 m

Explanation:

For two displacements two we can have several results, let's analyze each one of them

- collineal vectors, in the same direction

      R = A + B

      R = 20 +6

      R = 26 m

- Vectors in the opposite direction

     R = A-B

     R = 20-6

     R = 14 m

- angled vactors

    R = √ (A² + B²)

    R = √( 20² + 6²)

    R = 20.88 m

We can see that the displacements are maximum and minimum when the vectors are collinear