If overrightarrow A × overrightarrow B = overrightarrow C + overrightarrow D, then selec

Gujarati

Hindi

3-1.Vectors

medium

If $\overrightarrow A \times \overrightarrow B = \overrightarrow C + \overrightarrow D,$ then select the correct alternative-

$\overrightarrow B$ is parallel to $\overrightarrow C + \overrightarrow D$

$\overrightarrow A$ is perpendicular to $\overrightarrow C$

Component of $\overrightarrow C$ along $\overrightarrow A = $ component of $\overrightarrow D$ along $\overrightarrow A$

Component of $\overrightarrow C$ along $\overrightarrow A = -$ component of $\overrightarrow D $ along $\overrightarrow A$

According to definition of $cross-product$

$\overrightarrow{\mathrm{C}}+\overrightarrow{\mathrm{D}}$ is perpendicular to both $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$

i.e. $\quad \vec{A} \cdot(\vec{C}+\vec{D})=0$

or $\quad \overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{C}}+\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{D}}=0$

or $\quad$ A (component of $\overrightarrow{\mathrm{C}}$ along $\overrightarrow{\mathrm{A}}$ ) $+\mathrm{A}$

(component of $\overrightarrow{\mathrm{D}} \text { along } \overrightarrow{\mathrm{A}})=0$

or component of $\overrightarrow{\mathrm{C}}$ along $\overrightarrow{\mathrm{A}}$

$=$ $-$ component of $\overrightarrow{\mathrm{D}}$ along $\overrightarrow{\mathrm{A}}$

Standard 11

Physics

medium