R1 and R2 are two-position vectors making angles θ1 and θ2 with positive X-axis respectively. Their vector product is:[R1 = 4 cm, R2 = 3 cm , θ1 = 30 degrees , θ2 = 90 ]
Correct answer: B. 6√3
- A. 12√3
- B. 6√3
- C. 6√12
- D. 12√6
- E. 3√6
Explanation
The vector product of two vectors, R1 and R2, is given by the formula |R1 × R2| = |R1| |R2| sin(θ2 - θ1), where θ is the angle between the vectors. Here, |R1| = 4 cm, |R2| = 3 cm, θ1 = 30°, and θ2 = 90°. Thus, |R1 × R2| = 4 × 3 × sin(90° - 30°) = 4 × 3 × 1/2√3 = 6√3 cm.This calculation confirms that the correct answer is 6√3 cm, directed along the Z-axis.The incorrect options result from errors in either the trigonometric calculations or angle substitutions, leading to incorrect values.
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