In an octagon ABCDEFGH of equal side, what is the sum of
Question:

In an octagon $\mathrm{ABCDEFGH}$ of equal side, what is the sum of

$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}+\overrightarrow{\mathrm{AG}}+\overrightarrow{\mathrm{AH}}$

If, $\overrightarrow{\mathrm{AO}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$

  1. (1) $16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}-32 \hat{\mathrm{k}}$

  2. (2) $-16 \hat{\mathrm{i}}-24 \hat{\mathrm{j}}-32 \hat{\mathrm{k}}$

  3. (3) $-16 \hat{\mathrm{i}}-24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$

  4. (4) $-16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$


Correct Option: 1

Solution:

(1)

$\overrightarrow{A O}+\overrightarrow{O B}=\overrightarrow{A B}$

$\overrightarrow{A O}+\overrightarrow{O C}=\overrightarrow{A C}$

$\overrightarrow{A O}+\overrightarrow{O D}=\overline{A D}$

$\overrightarrow{A O}+\overrightarrow{O E}=\overrightarrow{A E}$

$\overrightarrow{A O}+\overrightarrow{O F}=\overrightarrow{A F}$

$\overrightarrow{A O}+\overrightarrow{O G}=\overrightarrow{A G}$

$\overrightarrow{A O}+\overrightarrow{O H}=\overrightarrow{A H}$

$8 \overrightarrow{\mathrm{AO}}=(\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}+\overrightarrow{\mathrm{AG}}+\overrightarrow{\mathrm{AH}})$

$=8(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})$

$=16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}-32 \hat{\mathrm{k}}$

Administrator

Leave a comment

Please enter comment.
Please enter your name.