What is the cross product of #[2, 1, -4]# and #[4,3,6] #?

Answer 1

(18,-28,2)

The simplest way to compute a three-dimensional cross product is to use the "cover up method." First and foremost, keep in mind that the cross product will always result in a new vector; therefore, if your answer is a scalar quantity, you have done something incorrectly.

As shown below, arrange the two vectors in a 3 x 3 determinant:

I, J, K, and I || 2 1 – 4 || 4 3 – 6 |

Next, covering the upper row and leftmost column starting from the left, you are left with: | 1 4 | | 3 6 |

To determine your i term, take this determinant:

#(1) * (6)-(3)*(-4) = 18#

For the j term, repeat the process by covering the middle column; for the k term, cover the right column.

Finally add the three terms together in a pattern of #+, -, +#

This results in:

#18 hat x - 28 hat i + 2 hat j#

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Answer 2

Olivia Askew

The cross product of [2, 1, -4] and [4,3,6] is [18, -32, 5].

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.