The figure formed by the four points ({i}+{j}-{k}),(2{i}+3{j}),(5{j}-2{k}) and ({k}-{j})

Correct Answer is : Quadrilateral

Correct Answer is : Quadrilateral

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AP EAPCET 23-Aug-2021 Shift 2 Paper

Section: Mathematics

Question : 28 of 160

Marks: +1, -0

(\hat{i}+\hat{j}-\hat{k}),(2\hat{i}+3\hat{j}),(5\hat{j}-2\hat{k})

(\hat{k}-\hat{j})

Solution:

Let

boOA=\hat{i}+\hat{j}-\hat{k}

bo OB=2\hat{i}+3\hat{j}

boOC=5\hat{j}-2\hat{k}

bo OD=\hat{k}-\hat{j}

\therefore boAB=boOB-boOA

=\hat{i}+\hat{2j}+\hat{k}

\Rightarrow |bo AB|=\sqrt{1^2+2^2+1^2}=\sqrt{6}

boBC=boOC-boOB

=-\hat{2i}+\hat{2j}-\hat{2k}

\Rightarrow |boBC|=\sqrt{(-2)^2+2^2+(-2)^2}=2\sqrt{3}

boCD=boOD-boOC

=-\hat{6j}+\hat{3k}

\Rightarrow |boCD|=3\sqrt{5}

boDA=boOA-boOD

=\hat{i}+\hat{2j}-\hat{2k}

\Rightarrow |boDA|=3

∵ All the sides has different length and no two sides are equal and parallel.

Hence, it forms only quadrilateral.

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