Question

A vector+ b vectro + cvector=0 then prove that avector*bvector=bvector*cvector

Answer 1

Please see the attachment

Answer 2

Answer:

$\bf\underline{Given}-$

$\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C} = 0$

$\bf\underline{To\;prove} -$

$\overrightarrow{A}×\overrightarrow{B}= \overrightarrow{B}×\overrightarrow{C}$

$\bf\underline{Proof}-$

$\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C} = 0$

$\overrightarrow{A}×{(\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C})} = 0$

$\overrightarrow{A}×\overrightarrow{A}+\overrightarrow{A}×\overrightarrow{B}+\overrightarrow{A}×\overrightarrow{C} = \overrightarrow{A}×0$

$0+\overrightarrow{A}×\overrightarrow{B}+\overrightarrow{A}×\overrightarrow{C} = \overrightarrow{A}×0$

$\overrightarrow{A}×\overrightarrow{B}+\overrightarrow{A}×\overrightarrow{C} = 0$

$\overrightarrow{A}×\overrightarrow{B}= -\overrightarrow{A}×\overrightarrow{C}$

$\overrightarrow{A}×\overrightarrow{B}= \overrightarrow{C}×\overrightarrow{A}$