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Question

A=(0,1,2),B=(3,0,1),C=(4,3,6),D=(2,3,2) are the rectangular cartesian co-ordinates. Find the area of the triangle ABC.

A
90,
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B
452
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C
45
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D
18
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Solution

The correct option is B 90,
Given, A=(0,1,2),B=(3,0,1),C=(4,3,6),D=(2,3,2)

AB=(30)i+(01)j+(12)k
AB=3i1j1k

AC=(40)i+(31)j+(62)k
AC=4i+2j+4k

Area of triangle ABC is =12|AB×AC|
AB×AC=∣ ∣ijk311424∣ ∣=2i16j+10k=2(i8j+5k)
Required area is =12|AB×AC|=90

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