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

Answer 1

#a#x#b=-10i-8j+3k#

Let vector #a=2*i-1*j+4*k# and #b=-1*i+2*j+2*k#

The cross-product formula

#a#x#b=[(i,j,k),(a_1,a_2,a_3),(b_1,b_2,b_3)]#
#a#x#b=+a_2b_3i+a_3b_1j+a_1b_2k-a_2b_1k-a_3b_2i-a_1b_3j#

Now let's solve the cross product.

#a#x#b=[(i,j,k),(2, -1, 4),(-1, 2, 2)]#
#a#x#b=#
#+(-1)(2)i+(4)(-1)j+(2)(2)k-(-1)(-1)k-(4)(2)i-(2)(2)j#
#a#x#b=-2*i-8i-4j-4j+4k-1*k#
#a#x#b=-10i-8j+3k#

Blessings...I hope this clarification is helpful.

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Answer 2

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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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.

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.

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