Using vectors, find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5)

Using vectors, find the area of the triangle with vertices A(1, 2, 3), B(2, -1, 4) and C(4, 5, -1)

The given points are : A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5)

Let O be the origin.

Position vector of A = OA = i^+j^+2k^position vector of B = OB = 2i^+3j^+5k^position vector of C = OC = i^+5j^+5k^AB =  OB - OA = i^+2j^+3k^AC =  OC- OA =4j^+3k^



Area =12|ABXAC|Now, ABXAC = i^j^k^123043 = -6i^-3j^+4k^Area=12|-6i^-3j^+4k^|=1236+9+16=612 sq units

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write the given pts in vector form then find AB(vector)*BC(vector) next find the modulus value of the found value at last use area of triangle formula =1/2*base*height= 1/2*AB(vector)*BC(vector)

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