If 2^i+3^j+4^k and ^i−^j+^kare two adjacent sides of a parallelogram, then the area of the parallelogram will be
A
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B
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C
Cannot be calculated from the given data
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D
none of the above
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Solution
The correct option is B We know that when two adjacent sides of a parallelogram are given, the area of the parallelogram is given by the magnitude of the cross product of these two vectors. Here two given sides are 2^i+3^j+4^k and ^i−^j+^k So their cross product will be given by the following determinant ∣∣
∣
∣∣^i^j^k2341−11∣∣
∣
∣∣ =^i((3×1)−(4×−1)−^j(2×1)−(4×1)+^k(2×−1)−(3×1)) =7^i+2^j−5^k Now the modulus of this cross product i.e. 7^i+2^j−5^k, will give you the area of the parallelogram. |7^i+2^j−5^k|=√(7)2+(2)2+(−5)2 =√49+4+25 =√78 Which is nothing but the area of the given parallelogram