NCERT Class 12-Mathematics: Exemplar Chapter –4 Determinants Part 8

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Question 12:

Find the value of θ satisfying


We have,

Expanding along , we get

Now, we know that

But is not possible

Question 13:

If then find values of .



Question 14:

If are in G.P., then prove that the determinant is independent of r.


We know that,

Where term of a First term of a GP and Common ratio of GP

We have

Question 15:

Show that the points, and do not lie on a straight line for any value of a.


Given, the point are

Hence, given points form a triangle i.e. points do not lie in a straight line.