If A⃗ and B⃗ are two vectors satisfying the relation A⃗ . B⃗ = |A⃗× B⃗|. Then the value of |A⃗-B⃗| will be :

Solution

Physics sir · 4 steps

Dot product equals the size of the cross product, so cos θ = sin θ and the angle is 45°.

1. Find the angle. Write both sides with the angle θ between the vectors: AB cos θ = AB sin θ. So tan θ = 1, which gives θ = 45° and cos θ = 1/√2.
2. Square the difference. For the magnitude of a difference, expand (A⃗-B⃗)·(A⃗-B⃗). The cross term comes with a minus sign.

   |A⃗-B⃗|² = A² + B² - 2AB cos θ

3. Put in the angle. 2AB cos 45° = 2AB × 1/√2 = √2AB. So |A⃗-B⃗|² = A² + B² - √2AB.
4. So. |A⃗-B⃗| = √(A² + B² - √2AB), which is option (c).

The idea to keep. When a dot product and a cross product are linked, compare cos θ with sin θ to get the angle first. Then use |A⃗±B⃗|² = A² + B² ± 2AB cos θ.

Answer from the NTA final answer key. Solution by PrepWiser.