MHT CET20242 May 2024Evening ShiftMathematicsVector AlgebraActual

The area of the triangle, whose vertices are A (1,-1,2), B (2,1,-1) and C (3,-1,2) , is

Options

A2 3 sq.units
B4 13 sq.units
C13 sq.units
D4 3 sq.units

Correct answer

C. 13 sq.units

Step-by-step solution

aligned & a = i - j +2 k , b =2 i + j - k , c =3 i - j +2 k & AB = b - a = i +2 j -3 k & AC = c - a =2 i aligned array ll & Area of triangle = 1 2 | AB AC | & AB AC = | array ccc i & j & k 1 & 2 & -3 2 & 0 & 0 array |=-6 j -4 k & | AB AC |= 36+16 = 52 =2 13 & Area of triangle = 1 2 (2 13 )= 13 sq. units array

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