Question

How far is the star \( V \) from star \( A \)?

Hint:

To find the distance between two points, use the magnitude of the difference of their position vectors.

Answer 1

Step 1: Compute the position vector of \( \overrightarrow{AV} \)
\[ \overrightarrow{AV} = \text{Position vector of } V - \text{Position vector of } A \] \[ \overrightarrow{AV} = (-3\hat{i} + 7\hat{j} + 11\hat{k}) - (7\hat{i} + 5\hat{j} + 8\hat{k}) = -10\hat{i} + 2\hat{j} + 3\hat{k}. \] Step 2: Compute the magnitude of \( \overrightarrow{AV} \)
\[ |\overrightarrow{AV}| = \sqrt{(-10)^2 + 2^2 + 3^2} = \sqrt{100 + 4 + 9} = \sqrt{113}. \] Step 3: Final result
The distance between star \( V \) and star \( A \) is \( \sqrt{113} \) units.