Question

Find the discussion thread for a math problem involving the dimensions of a rectangular roof and express the vector OD in terms of unit vectors i, j and k.

Answer 1

To express the vector \( \vec{OD} \) in terms of unit vectors \( \hat{i}, \hat{j}, \) and \( \hat{k} \), we first need to know the coordinates of point \( O \) and point \( D \).

Assuming the points are defined in a three-dimensional space, we can denote:
- Point \( O \) as \( O(x_1, y_1, z_1) \)
- Point \( D \) as \( D(x_2, y_2, z_2) \)

The vector \( \vec{OD} \) can be found using the formula:
\[
\vec{OD} = \vec{D} - \vec{O} = (x_2 - x_1)\hat{i} + (y_2 - y_1)\hat{j} + (z_2 - z_1)\hat{k}
\]

This expression gives the vector \( \vec{OD} \) in terms of the unit vectors \( \hat{i}, \hat{j}, \) and \( \hat{k} \).

Please provide the coordinates for points \( O \) and \( D \) if you want a specific numerical expression for \( \vec{OD} \).