# NCERT Class 12-Mathematics: Exemplar Chapter –4 Determinants Part 7

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**Question 9:**

**Answer:**

We have to prove,

Hence proved.

**Question 10:**

If then prove that

**Answer:**

We have,

Hence proved.

**Question 11:**

If the co-ordinates of the vertices of an equilateral triangle with sides of length are , then

**Answer:**

Since, we know that area of a triangle with vertices and is

Given by

We know that, area of an equilateral triangle with side a,

From Eq. (i) and (ii),

Hence proved