Question 75: Motion in 2D & Vectors

Question

In an octagon ABCDEFGH of equal side, what is the sum of
$$\overrightarrow {AB}  + \overrightarrow {AC}  + \overrightarrow {AD}  + \overrightarrow {AE}  + \overrightarrow {AF}  + \overrightarrow {AG}  + \overrightarrow {AH} $$,
if, $$\overrightarrow {AO}  = 2\widehat i + 3\widehat j - 4\widehat k$$

Accepted Answer

We know,
$$ \because $$ $$\overrightarrow {OA}  + \overrightarrow {OB}  + \overrightarrow {OC}  + \overrightarrow {OD}  + \overrightarrow {OE}  + \overrightarrow {OF}  + \overrightarrow {OG}  + \overrightarrow {OH}  = \overrightarrow 0 $$
By triangle law of vector addition, we can write
$$\overrightarrow {AB}  = \overrightarrow {AO}  + \overrightarrow {OB} \,;\,\overrightarrow {AC}  = \overrightarrow {AO}  + \overrightarrow {OC} $$
$$\overrightarrow {AD}  = \overrightarrow {AO}  + \overrightarrow {OD} \,;\,\overrightarrow {AE}  = \overrightarrow {AO}  + \overrightarrow {OE} $$
$$\overrightarrow {AF}  = \overrightarrow {AO}  + \overrightarrow {OF} \,;\,\overrightarrow {AG}  = \overrightarrow {AO}  + \overrightarrow {OG} $$
$$\overrightarrow {AH}  = \overrightarrow {AO}  + \overrightarrow {OH} $$
Now
$$\overrightarrow {AB}  + \overrightarrow {AC}  + \overrightarrow {AD}  + \overrightarrow {AE}  + \overrightarrow {AF}  + \overrightarrow {AG}  + \overrightarrow {AH} $$
$$ = (7\overrightarrow {AO} ) + \overrightarrow {OB}  + \overrightarrow {OC}  + \overrightarrow {OD}  + \overrightarrow {OE}  + \overrightarrow {OF}  + \overrightarrow {OG}  + \overrightarrow {OH} $$
$$ = (7\overrightarrow {AO} ) + \overrightarrow 0  - \overrightarrow {OA} $$
$$ = (7\overrightarrow {AO} ) + \overrightarrow {AO} $$
$$ = 8\overrightarrow {AO}  = 8(2\widehat i + 3\widehat j - 4\widehat k)$$
$$ = 16\widehat i + 24\widehat j - 32\widehat k$$

Answer

$$ - 16\widehat i - 24\widehat j + 32\widehat k$$

Answer

$$16\widehat i + 24\widehat j - 32\widehat k$$

Answer

$$16\widehat i + 24\widehat j + 32\widehat k$$

Answer

$$16\widehat i - 24\widehat j + 32\widehat k$$

Motion in 2D & Vectors

In an octagon ABCDEFGH of equal side, what is the sum of $\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH} , if, \overrightarrow {AO} = 2\widehat i + 3\widehat j - 4\widehat k

Choose the correct answer: