Thread: Very Urgent: (distances of vectors)

1) Find the coordinates of the foot of the perpendicular from Q(3,2,4) to the line r= (-6,-7,-3) +t(5,3,4)

2) The common perpendicular of two skew lines with the direction vectors d1 and d2 is the line that intersects both the skew lines and has direction vector n= d1 x d2. Find the points of intersection fo the common perpendicular with each of the lines (x,y,z)=(0,-1,0) + s(1,2,1) and
(x,y,z)= (-2,2,0) + t(2,-1,2)

These were assigned tonight and this content will be on tomorrows test I have no idea what to do. We've been studying distance between vectors,planes and points, but I can't do these at all.

Thanks!

Originally Posted by white_cap

1) Find the coordinates of the foot of the perpendicular from Q(3,2,4) to the line r= (-6,-7,-3) +t(5,3,4)

...

1. Create a plane perpendicular to the line containing Q:



2. Calculate the point of intersection between the line and the plane:







3. Plug in this value into the equation of the line. You'll get F(4, -1, 5)

Originally Posted by white_cap

...

2) The common perpendicular of two skew lines with the direction vectors d1 and d2 is the line that intersects both the skew lines and has direction vector n= d1 x d2. Find the points of intersection fo the common perpendicular with each of the lines (x,y,z)=(0,-1,0) + s(1,2,1) and
(x,y,z)= (-2,2,0) + t(2,-1,2)

...

1. Calculate the normal vector to the 2 direction vectors:



2. Calculate the equation of a line through a point of in the direction of :



3. Calculate the point of intersection :



4. You have now a system of simultaneous equations in 3 variables. I don't know how you solve such a system but you should get:



5. Plug in s into the equation of to get A(1, 1, 1)
and plug in t into the equation of to get B(0, 1, 2)