If a → = i ˙ ^ + j ˙ ^ + k ^ , b → = i ˙ ^ + 3 j ˙ ^ + 5 k ^ and c → = 7 i ˙ ^ + 9 j ˙ ^ + 11 k ^ then the area of parallelogram having diagonals a → + b → and b → + c → is

Question

If a → = i ˙ ^ + j ˙ ^ + k ^ , b → = i ˙ ^ + 3 j ˙ ^ + 5 k ^ and c → = 7 i ˙ ^ + 9 j ˙ ^ + 11 k ^ then the area of parallelogram having diagonals a → + b → and b → + c → is, 4 6 sq units, 1 2 21 s q u n i t s, 6 2 s q u n i t s, 6 sq units

MARKS App · Accepted Answer

Let A → = a → + b → = i ˙ ^ + j ˙ ^ + k ^ + i ˙ ^ + 3 j ˙ ^ + 5 k ^ = 2 i ˙ ^ + 4 j ˙ ^ + 6 k ^ a n d B → = b → + c → = i ˙ ^ + 3 j ˙ ^ + 5 k ^ + 7 i ˙ ^ + 9 j ˙ ^ + 11 k ^ = 8 i ˙ ^ + 12 j ˙ ^ + 16 k ^ ∴ A r e a o f p a r a l l e l o g r a m = 1 2 | | A → × B → | | = 1 2 i ˙ ^ j ˙ ^ k ^ 2 4 6 8 12 16 = 1 2 | - 8 i ˙ ^ + 16 j ˙ ^ - 8 k ^ | = ( - 4 ) 2 + ( 8 ) 2 + ( - 4 ) 2 = 4 6 sq units

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