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# NCERT

Q12   Area of a rectangle having vertices A, B, C and D with position vectors 

 - \hat i + \frac{1}{2} \hat j + 4 \hat k , \hat i + \frac{1}{2} \hat j + 4 \hat k , \hat i - \frac{1}{2}\hat j + 4 \hat k \: \: and \: \: - \hat i - \frac{1}{2} \hat j + 4 \hat k

 (A)1/2 

 (B) 1

 (C) 2

 (D) 4

Answers (1)
P Pankaj Sanodiya

Given 4 vertices of rectangle are 

\\\vec a=- \hat i + \frac{1}{2} \hat j + 4 \hat k , \\\vec b=\hat i + \frac{1}{2} \hat j + 4 \hat k , \\\vec c= \hat i - \frac{1}{2}\hat j + 4 \hat k \: \: and \: \: \\\vec d= - \hat i - \frac{1}{2} \hat j + 4 \hat k

\vec {AB}=\vec b-\vec a=(1+1)\hat i+(\frac{1}{2}-\frac{1}{2})\hat j+(4-4)\hat k=2\hat i

\vec {BC}=\vec c-\vec b=(1-1)\hat i+(-\frac{1}{2}-\frac{1}{2})\hat j+(4-4)\hat k=-\hat j

Now,

Area of the Rectangle 

A=|\vec {AB}\times\vec {BC}|=|2\hat i \times (-\hat j)|=2

Hence option C is correct.

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