Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are such that $\vec{A} \cdot \vec{B}=\vec{A} \cdot \vec{C}=0$…

Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ are such that $\vec{A} \cdot \vec{B}=\vec{A} \cdot \vec{C}=0$, then $\vec{A}$ is parallel to $\left[\cos 90^{\circ}=0\right]$
  1. $\overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{C}}$
  2. $\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}}$
  3. $\overrightarrow{\mathrm{C}}$
  4. $\overrightarrow{\mathrm{B}}$

Solution

Given that: $\vec{A} \cdot \vec{B}=0, \quad \vec{A} \cdot \vec{C}=0$ This means that vectors $\vec{A}, \vec{B}$, and $\vec{C}$ are all orthogonal to each other. Therefore, the vector $\vec{A}$ is perpendicular to both $\vec{B}$ and $\vec{C}$. The correct answer suggests that $\vec{A}$ is parallel to the vector that would satisfy this condition, making Answer: (2) correct.

Asked in: MHT CET 2020 (12 Oct Shift 2)

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