The components of a vector V can be written (Vx, Vy, Vz).

What are the components and length of a vector which is the sum of the two vectors, V1 and V2, whose components are (5.0, 1.3, -15.0) and (2.3, -4.7, -1.0)?

Vx = 5.0+2.3

Vy = 1.3-4.7
Vz = -16

length = sqrt (Vx^2+Vy^2+Vz^2)

Add the components for the vector sum

You get (7.3, -3.4, -16.0)

The length of any vector is the square root of the sum of the squares of the components.

Well, it looks like you've got some vectors V1 and V2 with their corresponding components. To find the sum of these vectors, you simply add their respective components. So, the components of the sum vector V would be:

Vx = V1x + V2x = 5.0 + 2.3 = 7.3
Vy = V1y + V2y = 1.3 + (-4.7) = -3.4
Vz = V1z + V2z = -15.0 + (-1.0) = -16.0

Now, to calculate the length of this sum vector, you can use the good ol' Pythagorean theorem. The length L of a vector in three dimensions is given by:

L = sqrt(Vx^2 + Vy^2 + Vz^2)

So, plugging in the values we found earlier:

L = sqrt(7.3^2 + (-3.4)^2 + (-16.0)^2)

L = sqrt(53.29 + 11.56 + 256)

L = sqrt(320.85)

L ≈ 17.91 (approximately)

So, the components of the sum vector are (7.3, -3.4, -16.0) and its length is approximately 17.91.

To find the sum of two vectors, V1 and V2, we simply add their corresponding components.

The components of V1 are (5.0, 1.3, -15.0).
The components of V2 are (2.3, -4.7, -1.0).

To find the components of the sum vector V, we add the corresponding components:

Vx = V1x + V2x = 5.0 + 2.3 = 7.3
Vy = V1y + V2y = 1.3 + (-4.7) = -3.4
Vz = V1z + V2z = -15.0 + (-1.0) = -16.0

Therefore, the components of the sum vector V are (7.3, -3.4, -16.0).

To find the length of the sum vector V, we can use the formula:

|V| = √(Vx^2 + Vy^2 + Vz^2)

Substituting the values:
|V| = √(7.3^2 + (-3.4)^2 + (-16.0)^2)
= √(53.29 + 11.56 + 256)
= √(320.85)
≈ 17.91 (rounded to two decimal places)

Therefore, the length of the sum vector V is approximately 17.91.

To find the sum of two vectors V1 and V2, you need to add their respective components together. Given that V1 = (5.0, 1.3, -15.0) and V2 = (2.3, -4.7, -1.0), you can calculate the sum as follows:

Sum of V1 and V2:
V = (V1x + V2x, V1y + V2y, V1z + V2z)

Using the given components:

V = (5.0 + 2.3, 1.3 + (-4.7), -15.0 + (-1.0))
= (7.3, -3.4, -16.0)

So, the components of the vector V, which is the sum of V1 and V2, are (7.3, -3.4, -16.0).

To find the length of the vector V, you can use the formula for the magnitude of a vector:

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

Using the components of V:

|V| = sqrt(7.3^2 + (-3.4)^2 + (-16.0)^2)
= sqrt(53.29 + 11.56 + 256.0)
= sqrt(320.85)
≈ 17.91

Therefore, the length of the vector V, which is the sum of V1 and V2, is approximately 17.91.