Factor the expression using the GCF. 6x + 42

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

10) The second angle in a triangle is 3° less than twice the first angle. The third angle measure 8° more than

andre [41]

Answer:

35, 67 and 78

Step-by-step explanation:

the angles are:

n, 2n-3 and 2n+8

there are 180 degrees in a triangle, so adding those terms together will give us 180

5n + 5 = 180

180 - 5 = 175

5n = 175

175 / 5 = 35

n = 35

now we have n we can put it in to the formula we have for the angles at the start:

n = 35

2n - 3 = 67

2n + 8 = 78

so the angles are

35, 67 and 78

8 0

3 years ago

Sammy opened a college savings account. She opened the account with $85, and then

MrMuchimi

Answer:

C. s= 85m + 45

Step-by-step explanation:

Given data

She opened the account with $85

and deposited $85

The equation that best models the relationship is

s= 85m + 45

Hence option C is correct

8 0

3 years ago

ASAP ANSWER PLZ The chemicals in my swimming pool use a ratio of 5 tablets of chlorine for every 14 days. Which ratio shows the

aliina [53]

42days × (5tablets/14days ) =15 tablets

3 0

3 years ago

Read 2 more answers

A coordinate grid showing Number of Classes on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lin

Oksana_A [137]

The system of equations representing these costs are; y = 7.5x and y = 5.5x + 10

<h3>How to find the equation of a line?</h3>

The slope of the first line is;

m = (y2 - y1)/(x2 - x1)

m = (32 - 10)/(4 - 0)

m = 5.5

Now, the first coordinate has a y-intercept of 10. Thus, the equation here for the cost is; y = mx + c = 5.5x + 10

The slope of the second line is;

m = (y2 - y1)/(x2 - x1)

m = (15 - 0)/(2 - 0)

m = 7.5

Now, the first coordinate has a y-intercept of 0. Thus, the equation here for the cost is; y = mx + c = 7.5x + 0 = 7.5x

Thus, the system of equations representing these costs are;

y = 7.5x and y = 5.5x + 10

Read more about Equation of a line at; brainly.com/question/13763238

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5 0

2 years ago