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Lina20 [59]
1 year ago
15

I can't figure out how to do (i + j) x (i x j)for vector calc

Mathematics
1 answer:
Vinil7 [7]1 year ago
8 0

In three dimensions, the cross product of two vectors is defined as shown below

\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}

Then, solving the determinant

\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}

In our case,

\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}

Where we used the formula for AxB to calculate ixj.

Finally,

\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}

Thus, (i+j)x(ixj)=i-j

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Answer:

585/3 = 195 students

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Dividing 585 students by 3 pictures per student means that there are 585/3=195 students.

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Unfortunately, I can't do it on a graph here, but I will do it algebraically.
The solution on the graph will be the point of intersection of the two lines representing the equations.
y + 2.3 = 0.45x . . . . . (1)
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From (2), y = 3.9 - 2.1x
substituting for y in (1), we have:
3.9 - 2.1x + 2.3 = 0.45x
2.55x = 6.2
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Allison plays basketball and last season she made a total of 87 shots (two- or three-point shots). Her point total was 191 . How
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Answer:

She made 17 three-point shots.

Step-by-step explanation:

Let t represent the number of three-point shots she made.

Since, she made a total of 87 shots (two- or three-point shots), the number of two-point shots will be 87-t.

The points from three-point shots:

→ 3t   (1)

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→ 2(87-t)   (2)

Since, her total point was 191, the sum of equation 1 and equation 2 must be equal to 191.

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Answer:

The center of this circle is found at (4, -2) and the radius is 6.

Step-by-step explanation:

The equation for a circle in standard for is  ( x – h)² + ( y - k)² = r². In this equation, (h, k) is the center of the circle and r is the radius.

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