Vector Algebra
Direction Cosines and Direction Ratios
Grade 12
Question:
<p>Here, m = cos(π/4) = 1/√2 and n = cos(π/2) = 0. If l² + m² + n² = 1, find the value of l.</p>
Step-by-Step Solution
Key Concept: The sum of squares of direction cosines of any line equals 1. This fundamental property allows us to find the missing direction cosine.
Step 1: We are given the direction cosines where l, m, n satisfy: l^2 + m^2 + n^2 = 1 Step 2: Substitute m = 1/√2 and n = 0: l^2 + (1/√2)^2 + 0^2 = 1 l^2 + 1/2 = 1 Step 3: Solve for l: l^2 = 1 − 1/2 = 1/2 l = ±1/√2 ∴ l = ±1/√2
Correct Answer: ±1/√2