If A and B are two vectors satisfying the relation A B. =. Then the value of will be: (a) √(A² + B² + √(2)AB) (b) √(A² + B²) (c) √(A² + B² - √(2)AB) (d) √(A² + B² + 2AB)

Answer: (c). Given A · B = |A × B|, find |A - B|. ABcos θ = ABsin θ ⇒ θ = 45°. |A - B|² = A² + B² - 2ABcos 45° = A² + B² - √(2)AB So the answer is (c) √(A² + B² - √(2)AB).

If A and B are two vectors satisfying the relation A B. =. Then the… | JEE Main 2021 (20 Jul, Shift 1)

Q12JEE Main 2021 · 20 JUL · SHIFT 1Medium

Vector (Cross) Product

If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A} \quad \vec{B}$ . = . Then the value of will be:

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Answer: (c)

Given $\vec{A} \cdot \vec{B} = |\vec{A} \times \vec{B}|$ , find $|\vec{A} - \vec{B}|$ .
$AB\cos\theta = AB\sin\theta \Rightarrow \theta = 45^\circ$ .
$|\vec{A} - \vec{B}|^2 = A^2 + B^2 - 2AB\cos 45^\circ = A^2 + B^2 - \sqrt{2}AB$
So the answer is (c) $\sqrt{A^2 + B^2 - \sqrt{2}AB}$ .

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Vector (Cross) Product question from JEE Main 2021 (20 Jul, Shift 1)

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