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

The cross-product formula

Now let's solve the cross product.

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To find the cross product of two vectors, we can use the formula:

[ \mathbf{a} \times \mathbf{b} = \begin{bmatrix} a_2b_3 - a_3b_2 \ a_3b_1 - a_1b_3 \ a_1b_2 - a_2b_1 \end{bmatrix} ]

Using the given vectors (\mathbf{a} = [2, -1, 4]) and (\mathbf{b} = [-1, 2, 2]), we substitute the components into the formula:

[ \mathbf{a} \times \mathbf{b} = \begin{bmatrix} (-1)(2) - (4)(2) \ (4)(-1) - (2)(-1) \ (2)(2) - (-1)(-1) \end{bmatrix} ]

[ \mathbf{a} \times \mathbf{b} = \begin{bmatrix} -2 - 8 \ -4 + 2 \ 4 - 1 \end{bmatrix} ]

[ \mathbf{a} \times \mathbf{b} = \begin{bmatrix} -10 \ -2 \ 5 \end{bmatrix} ]

Therefore, the cross product of ([2, -1, 4]) and ([-1, 2, 2]) is ([-10, -2, 5]).

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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.

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.

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.

- What is the cross product of #[3, 1, -4]# and #[3, -4, 2] #?
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- You kick a soccer ball with a speed of 12 m/s at an angle of 21. How long does it take the ball to reach the top of its trajectory?

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