Given that OA = 3i – 2j + k and OB = 4i – j – 3k. Find the distance between points A and B to 2 decimal places.

To find the distance between points A and B, we can use the distance formula in three-dimensional space. The formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

Here, (x₁, y₁, z₁) are the coordinates of point A, and (x₂, y₂, z₂) are the coordinates of point B.

Given that OA = 3i – 2j + k and OB = 4i – j – 3k, we can identify the coordinates as follows:

Coordinates of A: (x₁, y₁, z₁) = (3, -2, 1)
Coordinates of B: (x₂, y₂, z₂) = (4, -1, -3)

Now, let's substitute the values into the formula and calculate the distance:

d = √((4 - 3)² + (-1 - (-2))² + (-3 - 1)²)
= √(1² + 1² + (-4)²)
= √(1 + 1 + 16)
= √18
≈ 4.24

Therefore, the distance between points A and B, to 2 decimal places, is approximately 4.24 units.