Vector Algebra
Vector Operations
Grade 12
Question:
<p>What should be added to vector <strong>a</strong> = 3<strong>i</strong> + 4<strong>j</strong> - 2<strong>k</strong> to get its resultant a unit vector <strong>i</strong>?</p>
<p>(a) -2<strong>i</strong> - 4<strong>j</strong> + 2<strong>k</strong></p>
<p>(b) -2<strong>i</strong> + 4<strong>j</strong> - 2<strong>k</strong></p>
<p>(c) 2</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: To find what should be added to a vector to get a desired resultant, subtract the original vector from the desired resultant.
Step 1: Let the vector to be added be x = i - a . Step 2: We need a + x = i . Step 3: Therefore, x = i - (3 i + 4 j - 2 k ) = i - 3 i - 4 j + 2 k = -2 i - 4 j + 2 k . ∴ Answer is (a).
Correct Answer: A