Vector Algebra
Parallel and Collinear Vectors
Grade 12
Question:
<p>Let <strong>a</strong> = 3<strong>i</strong> − 6<strong>j</strong> + <strong>k</strong> and <strong>b</strong> = 2<strong>i</strong> − 4<strong>j</strong> + l<strong>k</strong>. Since <strong>a</strong> and <strong>b</strong> are parallel, find the value of l.</p>
Step-by-Step Solution
Key Concept: Two vectors are parallel if one is a scalar multiple of the other. Comparing coefficients gives the scalar and hence the unknown component.
Step 1: If vectors a and b are parallel, then a = m b for some scalar m. Step 2: We have (3 i − 6 j + k ) = m(2 i − 4 j + l k ) Step 3: Comparing coefficients of i : 3 = 2m ⟹ m = 3/2 Step 4: Comparing coefficients of k : 1 = lm ⟹ l × (3/2) = 1 ⟹ l = 2/3 ∴ l = 2/3
Correct Answer: 3/2