7 {i} - 4 {j} + 7 {k}, {i} - 6 {j} + 10 {k}, = {i} - 3 {j} + 4 {k}, 5 {i} - {j} + 5 {k} respectively, then ABCD is

Correct Answer is : a quadrilateral which is not a parallelogram

a parallelogram but not rhombus

Correct Answer is : a quadrilateral which is not a parallelogram

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AP EAPCET 05-Jul-2022 Shift 2 Paper

Section: Mathematics

Question : 29 of 160

Marks: +1, -0

7 \overline{i} - 4 \overline{j} + 7 \overline{k}, \overline{i} - 6 \overline{j} + 10 \overline{k}, = \overline{i} - 3 \overline{j} + 4 \overline{k}, 5 \overline{i} - \overline{j} + 5 \overline{k}

ABCD

Solution: 👈: Video Solution

We have,

\; A B = \; \text{ Position vector of } \; B - \; \text{ Position vector of } \; A

\; = -6 \hat{i} - 2 \hat{j} + 3 \hat{k}

\; |A B| = \sqrt{36+4+9} = 7

\; B C = \; \text{ Position vector of } \; C - \; \text{ Position vector of } \; B

\; = -2 \hat{i} + 3 \hat{j} - 6 \hat{k}

\; |B C| = \sqrt{4+9+36} = 7

\; C D = 6 \hat{i} + 2 \hat{j} + \hat{k}

\; |CD| = \sqrt{36+4+1} = \sqrt{41}

\; DA = 2 \hat{i} - 3 \hat{j} + 2 \hat{k}

\; |D A| = \sqrt{4+9+4} = \sqrt{17}

\; A C \; = -8 \hat{i} + \hat{j} - 3 \hat{k}

\; = A B + B C

\therefore A B C D

is a quadrilateral which is not a parallelogram.

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