MHT CET202122 Sep 2021Morning ShiftMathematicsVector AlgebraActual

The plane x 2 + y 3 + z 4 =1 cuts the X -axis at A, Y-axis at C, then the area of ABC =

Options

A71 sq. units
B29 sq. units
C41 sq. units
D61 sq. units

Correct answer

D. 61 sq. units

Step-by-step solution

The vertices of triangle ABC are aligned & A =(2,0,0) ; B =(0,3,0) ; C =(0,0,4) & AB =-2 i +3 j and AC =-2 i +4 k & AB AC = | array ccc i & j & k -2 & 3 & 0 -2 & 0 & 4 array |= i (12)- j (-8)+ k (6)=12 i +8 j +6 k & A ( ABC )= 1 2 | AB AC | & = 1 2 ( 144+64+36 ) & = 61 sq. units & aligned

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