Vector Algebra
Right Handed and Left Handed Systems
Grade None
Question:
<p><strong>Example 31.</strong> The vectors <strong>c</strong>, <strong>a</strong> = x<strong>i</strong> + y<strong>j</strong> + z<strong>k</strong> and <strong>b</strong> = <strong>j</strong> are such that <strong>a</strong>, <strong>c</strong>, and <strong>b</strong> form a right handed system. Then <strong>c</strong> is:</p>
<p>(a) z<strong>i</strong> - x<strong>k</strong></p>
<p>(b) <strong>0</strong></p>
<p>(c) y<strong>j</strong></p>
<p>(d) -z<strong>i</strong> + x<strong>k</strong></p>
Step-by-Step Solution
Key Concept: In a right handed system, the third vector equals the cross product of the first two in the correct order: b × a = c.
Step 1: a , c , and b form a right handed system. Step 2: Hence, b × a = c Step 3: c = j × (x i + y j + z k ) Step 4: c = -x k + z i = z i - x k ∴ Answer is (a).
Correct Answer: A