the components of a vector V can be written (Vx,Vy,Vz). what are the components and length of a vector which is te sum of the 2 vectors, V1 and V2, whose components are (8,-3.7,0) and (3.9,-8.1,-4.4)?

Add the corresponding components to get the components of the sum vector.

The length is the square root of the sum of the squared components

how do i find the angle between the summed vector and the z axis in this reference frame?

The cosine of that angle is vertical component divided by the vector length.

They don't ask for that angle in your original question

Very well

To find the components of the sum of two vectors V1 and V2, you need to add the corresponding components of V1 and V2.

Given V1 = (8, -3.7, 0) and V2 = (3.9, -8.1, -4.4):

The x-component of the sum (Vx) will be:
Vx = V1x + V2x = 8 + 3.9 = 11.9

The y-component of the sum (Vy) will be:
Vy = V1y + V2y = -3.7 - 8.1 = -11.8

The z-component of the sum (Vz) will be:
Vz = V1z + V2z = 0 - 4.4 = -4.4

So, the components of the sum of V1 and V2 are (11.9, -11.8, -4.4).

To find the length of the vector, you can use the Pythagorean theorem. The length (magnitude, denoted as ||V|| or |V|) of a vector V with components (Vx, Vy, Vz) is given by:

|V| = sqrt(Vx^2 + Vy^2 + Vz^2)

Using the components we found earlier:

|V| = sqrt((11.9)^2 + (-11.8)^2 + (-4.4)^2)
= sqrt(141.61 + 139.24 + 19.36)
= sqrt(300.21)
≈ 17.32

Therefore, the length (magnitude) of the vector sum of V1 and V2 is approximately 17.32.