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Finding Area of a Triangle using Determinants (includes example) Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Finding Area of a Triangle using Determinants (includes example) Video Lecture - Mathematics (Maths) Class 12 - JEE

1. How do you find the area of a triangle using determinants?
Ans. To find the area of a triangle using determinants, you need to first find the coordinates of the three vertices of the triangle. Then, you can use the following formula: Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|, where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.
2. What is a determinant?
Ans. In linear algebra, a determinant is a scalar value that can be calculated from the elements of a square matrix. It provides important information about the matrix, such as whether it is invertible or singular. Determinants are commonly used in various mathematical calculations, including finding the area of a triangle.
3. Why use determinants to find the area of a triangle?
Ans. Determinants are used to find the area of a triangle because they provide a convenient and efficient method to calculate the area using the coordinates of the triangle's vertices. By using determinants, you can avoid the need for lengthy calculations involving trigonometry or other geometric formulas.
4. Can determinants be used for any type of triangle?
Ans. Yes, determinants can be used to find the area of any type of triangle, whether it is scalene, isosceles, or equilateral. The method remains the same – calculating the determinant using the coordinates of the triangle's vertices – regardless of the triangle's shape or size.
5. What are some other applications of determinants in geometry?
Ans. Determinants have various applications in geometry. They can be used to find the volume of a parallelepiped, determine if three points are collinear, solve systems of linear equations, and calculate the equation of a plane. Determinants play a fundamental role in many geometric calculations and are widely used in mathematics and physics.
204 videos|288 docs|139 tests

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