IbTrojan Posted March 29, 2015 Report Share Posted March 29, 2015 (edited) 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 Reply Link to post Share on other sites More sharing options...
IB_taking_over Posted March 29, 2015 Report Share Posted March 29, 2015 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=05t=-1t=-1/5 or -.2 Step 4: plug t into the x and y eqns 3+2(-.2)=xx= 2.6 4-3(-.2)=yy=4.6 Step 5: write out the point of intersection(2.6,4.6,0) If you want, I can workout #2 as well. 2 Reply Link to post Share on other sites More sharing options...
IbTrojan Posted March 29, 2015 Author Report Share Posted March 29, 2015 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 Reply Link to post Share on other sites More sharing options...
L'estrange98 Posted April 21, 2015 Report Share Posted April 21, 2015 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! Reply Link to post Share on other sites More sharing options...
Slovakov Posted April 21, 2015 Report Share Posted April 21, 2015 (edited) 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 Reply Link to post Share on other sites More sharing options...
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