A is a vector quantity such that |A| = non-zero constant. Which of the following expression is true for A? (a) A · A = 0 (b) A × A 0

Answer: (c). |A × A| = A²sin 0° = 0, so A × A is the null vector. A · A = A² ≠ 0, and a vector cannot be 0. So the answer is (c) A × A = 0.

A is a vector quantity such that |A| = non-zero constant. Which of… | JEE Main 2022 (25 Jun, Shift 1)

Q10JEE Main 2022 · 25 JUN · SHIFT 1Easy

Vector (Cross) Product

$\vec{A}$ is a vector quantity such that $|\vec{A}|$ = non-zero constant. Which of the following expression is true for $\vec{A}$ ?

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Answer: (c)

$|\vec{A} \times \vec{A}| = A^2\sin 0^\circ = 0$ , so $\vec{A} \times \vec{A}$ is the null vector.
$\vec{A} \cdot \vec{A} = A^2 \neq 0$ , and a vector cannot be $< 0$ or $> 0$ .
So the answer is (c) $\vec{A} \times \vec{A} = 0$ .