Q.

The area of the triangle formed by the points A(1,2,3) B(-2,1,4),C(3,4,-2)

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a

14194

b

12194

c

194

d

2194

answer is B.

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Detailed Solution

The given vertices are A(1,2,3) B(-2,1,4),C(3,4,-2) The area of the triangle formed by the points A,B,C is 12|AB¯×AC¯|AB¯=−3i−j+k,AC¯=2i+2j−5kthe area of the triangle is                         12|AB×AC|=12ijk−3−1122−5=12|(3i−13j−4k)|=129+169+16=1942Therefore, the area of the triangle is 1942 square units
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