What is the angle (in degrees) between the vectors $a = 2 i + 3 j + 4 k$ and $b = 5 i - 6 j + 2 k$ ?

medium MCQ 2 marks Class 12 · Mathematics · Vector Algebra

Answer

90°

The correct answer is 90° — Step 5: Verify by checking the given options; 90° is present.

Step-by-step solution

Step 1: Recall the dot product formula: $a \cdot b = ∣ a ∣ ∣ b ∣ cos θ$ .
Step 2: Compute the dot product: $2 \cdot 5 + 3 \cdot (- 6) + 4 \cdot 2 = 10 - 18 + 8 = 0$ .
Step 3: Notice that a zero dot product implies $cos θ = 0$ .
Step 4: Therefore $θ = 90°$ .
Step 5: Verify by checking the given options; 90° is present.

Common mistake: Computing the dot product incorrectly, leading to a non‑zero value and thus an incorrect angle.

Concept tested: Angle between vectors