A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are, respectively 4 hati+3 hatj- hatk and -3 hati+ hatj+ hatk then DE=

Question

A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are, respectively 4 hati+3 hatj- hatk and -3 hati+ hatj+ hatk then DE= (A) 7 hati+2 hatj-2 hatk (B) -7 hati-2 hatj+2 hatk (C) 3 hati- hatj- hatk (D) -4 hati-3 hatj+ hatk

Tardigrade Admin · Accepted Answer

overlineDE= overlineBA <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/fe65b08b6420d2a4f121859492d519a8-.jpeg" /> =(4 hati+3 hatj- hatk)-3(-3 hati+ hatj+ hatk) =7 hati+2 hatj-2 hatk

Q. A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are, respectively $4 \hat{i} + 3 \hat{j} - \hat{k}$ and $- 3 \hat{i} + \hat{j} + \hat{k} t h e n D E =$

$7 \hat{i} + 2 \hat{j} - 2 \hat{k}$

$- 7 \hat{i} - 2 \hat{j} + 2 \hat{k}$

$3 \hat{i} - \hat{j} - \hat{k}$

$- 4 \hat{i} - 3 \hat{j} + \hat{k}$

$\overline{D E} = \overline{B A}$

$= (4 \hat{i} + 3 \hat{j} - \hat{k}) - 3 (- 3 \hat{i} + \hat{j} + \hat{k})$
$= 7 \hat{i} + 2 \hat{j} - 2 \hat{k}$

Q. A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are, respectively 4i^+3j^​−k^ and −3i^+j^​+k^thenDE=

7i^+2j^​−2k^

−7i^−2j^​+2k^

3i^−j^​−k^

−4i^−3j^​+k^