They are congruent is the answer
Answer:
square units
Step-by-step explanation:
We are given that two vectors
u=<3,2,1>
v=<1,2,3>
We have to find the area of parallelogram determined by the given vectors
![\vec{u}=3\hat{i}+2\hat{j}+\hat{k}](https://tex.z-dn.net/?f=%5Cvec%7Bu%7D%3D3%5Chat%7Bi%7D%2B2%5Chat%7Bj%7D%2B%5Chat%7Bk%7D)
![\vec{v}=\hat{i}+2\hat{j}+3\hat{k}](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%3D%5Chat%7Bi%7D%2B2%5Chat%7Bj%7D%2B3%5Chat%7Bk%7D)
We know that area of parallelogram determined by two vectors a and b
![\mid {a\times b}\mid =\begin{vmatrix}1&j&k\\x_1&x_2&x_3\\x_4&x_5&x_6\end{vmatrix}](https://tex.z-dn.net/?f=%5Cmid%20%7Ba%5Ctimes%20b%7D%5Cmid%20%3D%5Cbegin%7Bvmatrix%7D1%26j%26k%5C%5Cx_1%26x_2%26x_3%5C%5Cx_4%26x_5%26x_6%5Cend%7Bvmatrix%7D)
Using this formula
![\mi{u\times v}\mid=\begin{vmatrix}i&j&k\\3&2&1\\1&2&3\end{vmatrix}](https://tex.z-dn.net/?f=%5Cmi%7Bu%5Ctimes%20v%7D%5Cmid%3D%5Cbegin%7Bvmatrix%7Di%26j%26k%5C%5C3%262%261%5C%5C1%262%263%5Cend%7Bvmatrix%7D)
![\mid{u\times v}\mid=\mid{\hat{i}(6-2)-\hat{j}(9-1)+\hat{k}(6-2)\mid](https://tex.z-dn.net/?f=%5Cmid%7Bu%5Ctimes%20v%7D%5Cmid%3D%5Cmid%7B%5Chat%7Bi%7D%286-2%29-%5Chat%7Bj%7D%289-1%29%2B%5Chat%7Bk%7D%286-2%29%5Cmid)
![\mid{u\times v}\mid=\mid{4i-6j+4k}\mid=\sqrt{4^2+(-6)^2+4^2}=4\sqrt6](https://tex.z-dn.net/?f=%5Cmid%7Bu%5Ctimes%20v%7D%5Cmid%3D%5Cmid%7B4i-6j%2B4k%7D%5Cmid%3D%5Csqrt%7B4%5E2%2B%28-6%29%5E2%2B4%5E2%7D%3D4%5Csqrt6)
Area of parallelogram=
square units
Answer:
Money Paid in Total = $45
Step-by-step explanation:
Firstly, the term Mark-up refers to the amount added to the cost price to cover the overheads and realize a profit.
A mark-up percentage is a percentage (%) that is used as a basis to determine the mark-up value.
Given
Cost of an Item = 60$
Markup % = 25% on cost
Hence, Mark up in $ = 60$*25%
= 15$
Therefore, Actual cost of an item = Cost of an item - Mark up on Item
= 60$ - 15$
= 45$
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Answer:
I think it's sit and reach sorry if I'm wrong
The probability is simply the chance you have of getting each color.
Therefore:
Black= 4/12 or 1/3
Blue or Red= 8/12 or 2/3