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Question

Let OA=a,OB=10a+2bandOC=b where O,AandC are non-collinear points. Let pdenote the area of the quadrilateral OABC and q denote the area of the parallelogram with OA and OC as adjacent sides. If p=kq then k is equal to?


A

4

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B

6

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C

0

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D

1

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Solution

The correct option is B

6


Explanation for correct option:

Finding the value of k:

Given, OA=a,OB=10a+2bandOC=b. Also, O,AandC are non-collinear points.

Now according to the question we have,

Area of parallelogram=q

q=a×b∵aandbareadjecentsides

Area of quadrilateral, OABC=p

p=areaof△OAB+areaof△OBC⇒p=12OA×OB+12OB×OC⇒p=12a×10a+2b+1210a+2b×b⇒p=122a×b+1210a×b∵a,barevectors⇒p=a×b+5a×b⇒p=6a×b⇒p=kqgiven

Comparing the above expression with the given expression, we get, k=6

Hence, the correct answer is option (B).


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