Calculate the area of the parallelogram when adjacent sides are given by the vectors $\to A =^i -^j + 2^k$ and $\to B = 2^i - 3^j + 4^k$

2^i -^k

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- 2^i -^k

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2^i +^k

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2^i - 2^k

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Solution

The correct option is A $2^i -^k$
We know that the area of parallelogram is given by $\to A \times \to B$ , where vectors are the adjacent sides.
Thus, area of parallelogram is given by
$⎡ ⎢ ⎣ \begin{matrix} ^i & ^j & ^k 1 & - 1 & 2 2 & - 3 & 4 \end{matrix} ⎤ ⎥ ⎦$
$\Rightarrow (- 4 - (- 6))^i - (4 - 4)^j + (- 3 - (- 2))^k$
$\Rightarrow 2^i -^k$

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Calculate the area of the parallelogram when adjacent sides are given by the vectors →A=^i−^j+2^k and →B=2^i−3^j+4^k

The correct option is A 2^i−^kWe know that the area of parallelogram is given by →A×→B, where vectors are the adjacent sides. Thus, area of parallelogram is given by ⎡⎢⎣^i^j^k1−122−34⎤⎥⎦ ⇒ (−4−(−6))^i−(4−4)^j+(−3−(−2))^k ⇒ 2^i−^k

Calculate the area of the parallelogram when adjacent sides are given by the vectors $\to A =^i -^j + 2^k$ and $\to B = 2^i - 3^j + 4^k$