Question

a vector v has components v, = 1, vy = 2, v, = -5. a vector w has components w, = 3, w, = -1, w, = 1. evaluate

Answer 1

To find the magnitude of the resultant vector when adding vectors u, v, and ŵ together, you need to add their respective components. The magnitude of the resultant vector is 2sqrt(2).

Step-by-step explanation:

To find the magnitude of the resultant vector when adding vectors u, v, and ŵ together, we need to add their respective components.

The components of vector u are ux = -1, uy = 1, and uz = 1.

The components of vectors v and w are given in the problem statement.

Adding the corresponding components, we get:

Resultant vector = (ux + vx + wx, uy + vy + wy, uz + vz + wz)

Substituting the given values, we have:

Resultant vector = (-1 + 3, 1 + (-1), 1 + 1) = (2, 0, 2)

To find the magnitude of the resultant vector, we can use the Pythagorean theorem:

|Resultant vector| =
`sqrt((2^2) + (0^2) + (2^2)) = sqrt(4 + 0 + 4)`

Therefore, the magnitude of the resultant vector is 2sqrt(2).