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In this problem, we are given two vectors and told that they form a parallelogram, and we are asked to determine the area of that parallelogram.
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To do this, we are first going to take the cross product of u cross v.
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And to do that, we're going to write a matrix with its first row as i, j, and k, and its second row with the components of u because we're doing u cross b.
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And its third row with the components of v.
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And when we do this, we get the following component for i.
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We're going to cross out the first column.
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Take the determinant of this 2x2 by 2 matrix.
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It's going to be 2 times 3 minus 1 times 2.
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That's going to be 6 minus 2.
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That's 4.
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Then we always subtract the component for j.
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And we're going to get the following.
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Cross out the middle column.
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Take the determinant of this 2 by 2 matrix...