Question Detail
Question
Vector A has magnitude 8 units in the direction of the positive x-axis, vector B has magnitude 6√3 units and lies in the x-y plane, making an angle 30° with the positive x-axis and 60° with the positive y-axis. Find the vector product A × B.
Correct Answer
Option A is the correct answer.
Detailed Explanation
A = 8i. B has magnitude 6√3. Its components: B_x = 6√3 cos30° = 6√3 * (√3/2) = 6*3/2 = 9. B_y = 6√3 cos60° = 6√3 * (1/2) = 3√3. B_z = 0. So B = 9i + 3√3 j. Then A × B = (8i) × (9i + 3√3 j) = 8i × 9i + 8i × 3√3 j = 0 + 24√3 (i×j) = 24√3 k.
Hint
Write vectors in component form and compute the cross product.