I need help please? As fast as possible.....

[XBOX999]

Hello,
I need help in these quetions. Please, show me all the steps to solve them. I want the final answer please.

1- Find the distence from a point P= ( -3,4,2) to a line Lx,y,z)= ( 3,-2,-1)+(1,-2,2)t.

2-find the equation in the form of ax+by+cz=d, of the plane going through a point
P= (-3,4,2) to a line Lx,y,z)= (3,-2,-1) + (1,-2,2)t.

3-Find all complex numbers z= a+bi with the property z^3 =-i

4-let x= 2e^-(?/4)i , y=3e^(?/6)i . Let a+bi= x^2/y^3 . Find a and b.

 

[galactus]

1- Find the distance from a point P= ( -3,4,2) to a line Lx,y,z)= ( 3,-2,-1)+(1,-2,2)t.

The line has equation \(\displaystyle x=3+t, \;\ y=-2-2t, \;\ z=-1+2t\)

The direction numbers are the numbers in front of the t's. So, we have u=[1,-2,2].

This gives the direction vector for the line.

To find a point on the line, let t=0. P=[3,-2,-1].

Therefore, \(\displaystyle PQ=(-3-3, \;\ 4-(-2), \;\ 2-(-1))=(-6, \;\ 6, \;\ 3)\)

Now, take the cross product of u and PQ, then use the distance formula for the distance between a point and a line.

Which is \(\displaystyle D=\frac{||PQ\times u||}{||u||}\)

 

[Denis]

Hello,
I need help in these quetions. Please, show me all the steps to solve them. I want the final answer please.

Did you read "Read before posting"?
This is not a classroom.

 

[Deleted member 4993]

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