Question

What position vector is equal to the vector from 13, 5, -22 to 10, -6, 32?

Answer 1

To find the position vector from (13, 5, -22) to (10, -6, 32), subtract the initial position vector from the final position vector. The position vector is (-3, -11, 54).

Step-by-step explanation:

To find the position vector equal to the vector from (13, 5, -22) to (10, -6, 32),

we need to subtract the initial position vector from the final position vector.

The position vector is given by the final coordinates minus the initial coordinates.

So, the position vector is (10, -6, 32) - (13, 5, -22) = (-3, -11, 54).

Answer 2

The position vector from (13, 5, -22) to (10, -6, 32) is calculated by subtracting the coordinates of the first point from the second, resulting in the vector (-3, -11, 54).

Step-by-step explanation:

To find the position vector from the point (13, 5, -22) to the point (10, -6, 32), follow these steps:

1. Subtract the coordinates of the first point from the coordinates of the second point to get the differences:

x-coordinate: (10 - 13) = -3

y-coordinate: (-6 - 5) = -11

z-coordinate: (32 - (-22)) = 54

2. Write these differences as a vector in component form:

[-3, -11, 54]

This vector represents the displacement or change in position between the two points.

3. To find the position vector from the first point to the second point, add this displacement vector to the position vector of the first point. The position vector of the second point is then equal to the sum of these two vectors.

The position vector of the first point is (13, 5, -22). Adding the displacement vector gives us:

[13, 5, -22] + [-3, -11, 54] = [10, -6, 32]

Therefore, the position vector from (13, 5, -22) to (10, -6, 32) is [7, -17, 86].