Another Vectors Question

[IbTrojan]

1) For the line defined the parametric equations x = 3 + 2t , y = 4 - 3t, z = 1 + 5t find the coordinates of where the line crosses the x-y plane.

 

2) Find the coordinates of the point where r = [-2, 5, 3] + t [-1, 2, 1] intersects the x-y plane. 

 

 

I don't get how to do them. Please help

Edited March 29, 2015 by IbTrojan

[IB_taking_over]

1)

 

Stuff that makes it easier to figure out the answer:

XY plane means that the point of intersection will be (x,y,0)

 

Vector eqn: [3 4 1] + t[2 -3 5]   

 

Step 1: set the eqn equal to the point

 

[3 4 1] + t[2 -3 5] = (x,y,0) 

 

Step 2: parametric eqns from step 1.

 

3+2t=x , 4-3t=y , 1+5t=0

 

Step 3: Solve for t

 

1+5t=0

5t=-1

t=-1/5 or -.2

 

Step 4: plug t into the x and y eqns

 

3+2(-.2)=x

x= 2.6

 

4-3(-.2)=y

y=4.6

 

Step 5: write out the point of intersection

(2.6,4.6,0)

 

 

If you want, I can workout #2 as well.

[IbTrojan]

 

 

If you want, I can workout #2 as well.

 

Thanks so much IB_taking_over!! I think it was just the x-y plane part that was throwing me off. 

 

I think I'll try #2 first and if I don't get it, I'll let you know. 

Thanks again

[L'estrange98]

Hi! I need help with this vector question:

A helicopter at A(6,9,3)  moves with constant velocity in straight line. 10 minutes later it is at B(3,10,2.5). Distances are in kilometers.

-Find the helicopters speed.

-The helicopter is traveling directly towards its helipad, which has z-coordinate 0. Find the total time taken from the helicopter to land.

 

Thank you so much!

[Slovakov]

The displacement vector is . To calculate speed (which is  a scalar) we need to find the length of this vector, i.e. These 3,2km were covered in 10 minutes, so its speed is some 19.2km/h (rather slow for a helicopter)

 

For the second part of the question, we only look at the last number in the vectors.We can see that the helicopter drops by 0.5km every 10 minutes, hence 3km/h. It needs to cover 3km from point A and 2.5km from point B to reach 0.  Now it's easy to deduce that it will need an hour to drop from point A, and 50 minutes from point B.

Edited April 21, 2015 by Slovakov