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Kamila [148]
3 years ago
9

Help me I really need this done

Mathematics
1 answer:
e-lub [12.9K]3 years ago
3 0

Answer: I think it's 24

Step-by-step explanation:

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I can't figure out how to do (i + j) x (i x j)for vector calc
Vinil7 [7]

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

8 0
1 year ago
Expressions that simplify to the same expression are called ____ expressions.
larisa86 [58]
They're called equivalent expressions
5 0
3 years ago
Read 2 more answers
Subtract (x² + 5x – 6) – (3x^2 – 7x + 1).<br> What is the difference?
Lorico [155]
1. Distribute the Negative Signs
2. Combine like terms
-2x^2 + 12x-7
4 0
3 years ago
Two sides of an isosceles triangle have lengths of 3 and 10. Find the length of the third side.
lora16 [44]

Answer:

The third side must be 10:  {3, 10, 10}; {10, 3, 3} is not possible.

Step-by-step explanation:

Everything depends on our understanding of "isosceles."

This term indicates that two sides of a given triangle are equal.

If two sides of an isosceles triangle have lengths of 3 and 10, then:

Either 1)  Two sides have length 10 and the third side has length 3.  This is certainly possible

or

2)  sides have length 3 and the third side has length 10.  This is NOT possible, since 3 + 3 adds up to 6, which is less than 10.

8 0
3 years ago
Grace and Jamal each bought notebooks for school. Grace bought 3 notebooks for $3.90 while Jamal bought 2 notebooks for $2.20. W
ludmilkaskok [199]
3.9/3=$1.30

2.2/2=$1.10

The unit prices are $1.30 and $1.10.
Hope this help!
7 0
3 years ago
Read 2 more answers
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