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  • Help me answer: The area of the quadrilateral ABCD , where A(0,4,1), B(2,3,-1), C(4,5,0) and D(2,6,2) is equal to

The area of the quadrilateral ABCD , where A(0,4,1), B(2,3,-1), C(4,5,0) and D(2,6,2) is equal to

  • Option 1)

    9 sq unit

  • Option 2)

    18 sq unit

  • Option 3)

    27 sq unit

  • Option 4)

    81 sq unit

 

Answers (1)

best_answer

As we learnt

Vector Representation -

Consider a point P(a,b,c) in space then the position vector of P will be

a\hat{i}+b\hat{j}+c\hat{k} .

-

 

 area (\Delta ABC)= \frac{1}{2}\left | \vec{AB} \times \vec{AC} \right |

                                \frac{1}{2}\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & -1 & -2\\ 4 & 1 & -1 \end{vmatrix} =\frac{1}{2} \times \sqrt{9 + 36+36} = \frac{9}{2}.....(i)

area (\Delta ADC)=\frac{1}{2} \left | \vec{AD} \times \vec{AC} \right |

 

\frac{1}{2}\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 2 & 1\\ 4 & 1 & -1 \end{vmatrix} =\frac{1}{2} \times \sqrt{9 + 36+36} = \frac{9}{2} .....(ii)

 

So, area of quadrilateral = 9 (Adding i & ii)


Option 1)

9 sq unit

correct

Option 2)

18 sq unit

incorrect

Option 3)

27 sq unit

incorrect

Option 4)

81 sq unit

incorrect

Posted by

prateek

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