Q. 185.0( 1 Vote )

Using vectors, fi

Answer :

Given three points A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5) forming a triangle.


Let position vectors of the vertices A, B and C of ΔABC be, and respectively.



We know position vector of a point (x, y, z) is given by, where, and are unit vectors along X, Y and Z directions.




Similarly, we have and


To find area of ΔABC, we need to find at least two sides of the triangle. So, we will find vectors and.


Recall the vector is given by







Similarly, the vector is given by







Recall the area of the triangle whose adjacent sides are given by the two vectors and is where



Here, we have (a1, a2, a3) = (1, 2, 3) and (b1, b2, b3) = (0, 4, 3)






Recall the magnitude of the vector is



Now, we find.






Thus, area of the triangle is square units.

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