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Question: If vertices of triangle are \(A ( 1 , - 1,2 )\), \(B ( 2,0 , - 1 )\) and \(C ( 0,2,1 )\), then the a...

If vertices of triangle are A(1,−1,2)A ( 1 , - 1,2 ), B(2,0,−1)B ( 2,0 , - 1 ) and C(0,2,1)C ( 0,2,1 ), then the area of triangle is

A

6\sqrt { 6 }

B

262 \sqrt { 6 }

C

363 \sqrt { 6 }

D

464 \sqrt { 6 }

Answer

262 \sqrt { 6 }

Explanation

Solution

⇒4i+2j+2k∣=16+4+4=24=26\Rightarrow 4 \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } \mid = \sqrt { 16 + 4 + 4 } = \sqrt { 24 } = 2 \sqrt { 6 }