Question

Vector question

Answer 1

I need help with part 3.
My method is to find the direction vector BA of the starting point of l1 and l3. Then find the dot product of BA with unit vector of line 1. Then apply pythagoras to find the perpendicular length. I know other methods which will work here. But why is this method incorrect?

Answer 2

What are the direction vectors of l1 and l3 ?

Answer 3

What do you know about the cross product of two vectors ?

Answer 4

Working
BA = (1 10 3) -(6 5 4) = (-5 5 -1)
Unit vector of Line 1 = 1/√3 (1 1 1)
BA. Unit vector of line 1 = 1/√3

Answer 5

@ganeshie8 I know the method you're implying. But I just want to know the fallacy in my method.

Answer 6

What's so special about the unit vector of line1 ?

Answer 7

Why didn't you use the other line for the unit vector ?

Answer 8

Yes, but what use is the projection of BA onto line1 ?

Answer 9

I suggest you draw two skewed lines first

Answer 10

Then BA² = projection on l1² +perpendicular²

Answer 11

Interesting, explain me your method using some pictures...

Answer 12

Oh I see ! That's really clever ! It should work perfectly

Answer 13

But it's not working

Answer 14

Yeah, unfortunately we're wrong. There is a mistake

Answer 15

What is it?

Answer 16

Maybe the varying magnitudes of BA?