Vectors and The Dot Product

1. Let \(\overrightarrow{v}=3\overrightarrow{i}-5\overrightarrow{j}\) and \( \overrightarrow{w}= -2\overrightarrow{i} + 3\overrightarrow{j}\). Find (a) \( ||\overrightarrow{v}-\overrightarrow{w}||\), and (b) \(||\overrightarrow{v}||+||\overrightarrow{w}||\)     SOLUTION

2. Let \(\overrightarrow{v}=2\overrightarrow{i} - 3\overrightarrow{j}\) and \(\overrightarrow{w}= -3\overrightarrow{i}+ 4\overrightarrow{j}\). Find  (a) \( ||\overrightarrow{v}-\overrightarrow{w}||\), and (b) \(||\overrightarrow{v}||-||\overrightarrow{w}||\)    SOLUTION

3. Find a unit vector in the same direction as \(\overrightarrow{v} = 3\overrightarrow{i}- 4\overrightarrow{j} \).   SOLUTION

4. Find the angle between the given vectors, and state whether they are parallel, orthogonal or neither.    SOLUTION

  \(\overrightarrow{u}=2\overrightarrow{i}+ \overrightarrow{j}, \quad \overrightarrow{v}=\overrightarrow{i} - 2\overrightarrow{j}\)

5. Find the angle between the given vectors, and state whether they are parallel, orthogonal or neither.     SOLUTION

  \(\overrightarrow{u}=2\overrightarrow{i}-5 \overrightarrow{j}, \quad \overrightarrow{v}=4\overrightarrow{i} - 10\overrightarrow{j}\)