Question

a times b is equal to

• A. ab sin θ
• B. ab cos θ
• C. ab sin θ n̂
• D. none of these

Hint:

The magnitude of the cross product of two vectors is given by |a × b| = ab sin θ, where θ is the angle between them.

Answer 1

The Correct Option is A

Step 1: Cross product formula. 
The magnitude of the cross product of two vectors a and b is given by the formula: |a × b| = ab sin θ where θ is the angle between the vectors a and b, and a and b are the magnitudes of the vectors.

Step 2: Explanation of other options. 
(A) ab sin θ : Correct. This is the correct formula for the magnitude of the cross product. 
(B) ab cos θ : Incorrect. This is not the correct formula for the cross product. It resembles the dot product formula. 
(C) ab sin θ n̂ : Incorrect. The unit vector n̂ is involved in the direction of the cross product, not in the magnitude. 
(D) none of these : Incorrect. Option (A) is correct. 

Step 3: Conclusion. 
The magnitude of the cross product |a × b| is given by ab sin θ, so the correct answer is (A). 

Final Answer: ab sin θ.