MHT CET20228 Aug 2022Morning ShiftMathematicsVector AlgebraActual

If the area of the triangle with vertices i +y j , i +2 k and 3 j + k is 6 sq. units, then the values of y are

Options

A2,4
B3,4
C-2,4
D2,-4

Correct answer

A. 2,4

Step-by-step solution

aligned & A B =( i +2 k )-( i +y j )=0 i -y j +2 k & B C =(3 j + k )-( i +2 k )=- i +3 j - k & Now area of triangle = 1 2 | A B B C |= 6 & 1 2 | array ccc i & j & k 0 & -y & 2 -1 & 3 & -1 array |= 6 & |(y-6) i -2 j -y k |=2 6 & (y-6)^2+(-2)^2+(-y)^2=(2 6 )^2 & y^2-12 y+36+4+y^2=24 & y^2-6 y+8=0 & y=2,4 aligned

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