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This question asks us to find the cross product of two vectors.
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The vectors we're given are a.
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Vector a is equal to 0, negative 4, 1, and b.
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Vector b is equal to 1, 1, negative 2.
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So we're going to find this cross product using the standard method where we will throw the coordinates into a 3x3 matrix with the first row being the unit vectors, i, j, and k.
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We'll find the determinant of this 3x3 matrix, and the determinant will give us scaled values for each of these unit vectors.
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When we add all of the scaled vectors together, we will get a cross -product of these two vectors.
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So let's jump into it.
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Remember, when we take the determinant of a 3x3 matrix, we will decompose by co -factors.
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What that means is we will choose a row.
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In this case, i'm going to choose row one.
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You could do it choosing row two or three, but it's going to be far easier to choose row one.
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I'll choose row one, and then for each element in this row, i'll find the cofactors, which are just the determinants of the matrix with the row and column of the individual element omitted.
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You'll see what i mean as i get into it.
01:29
So first i'm going to do i.
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When i do i, its co -factor is the determinant of this matrix multiplied by i.
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So that co -factor is going to be negative 4 times negative 2, which is positive 8, minus 1 times 1, which is just 1.
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That's the determinant of this matrix, which we call the minor, and it's multiplied by i, the unit vector i.
01:57
Next, we'll do the second co -factor, but there's a key distinction that we need to make here...