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Vesnalui [34]
3 years ago
6

Express the vector ModifyingAbove Upper P 1 Upper P 2 with right arrowP1P2 in the form Bold v equals v 1 Bold i plus v 2 Bold j

plus v 3 Bold kv=v1i+v2j+v3k if Upper P 1P1 is the point (0 comma 1 comma negative 3 )(0,1,−3) and Upper P 2P2 is the point (negative 5 comma negative 3 comma negative 9 )(−5,−3,−9).
Mathematics
1 answer:
Tatiana [17]3 years ago
3 0

Answer:

  \overrightarrow{P_1P_2}=-5\textbf{i}-4\textbf{j}-6\textbf{k}

Step-by-step explanation:

  \overrightarrow{P_1P_2}=(P_2-P_1)\cdot(\textbf{i},\textbf{j},\textbf{k})=(-5-0)\textbf{i}+(-3-1)\textbf{j}+(-9-(-3))\textbf{k}\\\\\overrightarrow{P_1P_2}=-5\textbf{i}-4\textbf{j}-6\textbf{k}

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Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point
Maksim231197 [3]

Answer: (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

or  (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]

Taking square on both the sides , we get

(x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0

Using quadratic formula : x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}

so, (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

since \sqrt{3}=1.732

so, (6+7(1.732),0)\text{ and }(6-7(1.732),0) are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

3 0
3 years ago
In a rectangular coordinate plane what is the distance between points (-3,0) and (3,8)
zheka24 [161]

To calculate the distance between two points, we can use a formula that is a variation Pythagorean Theorem. Look:


\mathsf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}


"d" represents the distance and coordinates are expressed as follows: (x, y)


Let's go to the calculations.


\mathsf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}\\\\ \mathsf{d=\sqrt{(3-(-3))^2+(8-0)^2}}\\\\ \mathsf{d=\sqrt{(3+3)^2+(8)^2}}\\\\ \mathsf{d=\sqrt{(6)^2+64}}\\\\ \mathsf{d=\sqrt{36+64}}\\\\ \mathsf{d=\sqrt{100}}\\\\ \underline{\mathsf{d=10}}


The answer is 10 uc.

8 0
4 years ago
Noah plays football. His team's goal is to score
OleMash [197]

Answer:

No

Step-by-step explanation:

We can plug in the ordered pair (6,-1) into the equation. Remember that 6 is the x coordinate therefore we plug it in for x and that -1 is the y coordinate so we should plug it in for y.

6x+3y=6(6)+3(-1)=36-3=33

Since 33 is not equivalent to 15, (6, -1) is not a solution to the equation.

3 0
2 years ago
370 is 125% of what number?
bonufazy [111]

Answer:

125/100 x N = 370

x 100 x 100

125n = 37,000 (since your multiplying what you got to the variable)

Divide by 125

N = 296

7 0
3 years ago
I will give brainlest
STALIN [3.7K]

Answer:

-360

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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