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Question -

Using the determinants prove that the points (a, b), (aтАЩ, bтАЩ) and (a тАУ aтАЩ, b тАУ b) are collinear if a bтАЩ = aтАЩ b.



Answer -

Given (a, b), (aтАЩ, bтАЩ)and (a тАУ aтАЩ, b тАУ b) are collinear

We have the conditionthat three points to be collinear, the area of the triangle formed by thesepoints will be zero. Now, we know that, vertices of a triangle are (x1,y1), (x2, y2) and (x3, y3),then the area of the triangle is given by,

тЗТ┬аa bтАЩ = aтАЩ b

Hence, the proof.

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