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Consider the following statements : 1...

Consider the following statements :
1. The determinants `|(1,a,bc),(1,b,ca),(1,c,ab)| and |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|` are not identically equal.
2. For `a gt 0, b gt 0, c gt 0` the value of the determinant `|(a,b,c),(b,c,a),(c,a,b)|` is always positive.
3. If `|(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|=|(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1)|`, then the two triangles with vertices `(x_(1),y_(1)), (x_(2),y_(2)), (x_(3), y_(3))` and `(a_(1),b_(1)), (a_(2), b_(2)), (a_(3), b_(3))` must be congruent. Which of the statement given above is/are correct?

A

Only (1)

B

Only (2)

C

Only (3)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
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