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# How do you work out this vector C4 question?

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1. Hi if possible could someone help me with this C4 vectors question. i've attached a pic of it - it's part cii which I'm struggling with

Basically, for starters I don't understand what 'foot of the perpendicular from A to L' means - I've looked it up, but I can't picture how it works on a diagram for this specific question. If anyone could explain that, it would be much appreciated
Then I'm not entirely sure how to do the question itself - could someone show me how you do it? I've looked at the mark scheme (and I've attached a pic of that too below) but I can't make sense of it
Attachment 525323525325

(Let me know if you can't view the picture of the mark scheme - it might show up in attached thumbnails)
Attached Images

2. bump
3. (Original post by Phoebus Apollo)
...
The blue line is the line , the red line is the one parallel to that through the point . The question is asking you to prove that, if you draw the perpendicular line starting from A on the red line and make that perpendicular touch the blue line, that the point it touches the blue line is the point B. As shown (in a hastily draw diagram, sorry!):

Does that clarify matters?
4. (Original post by Phoebus Apollo)
...
As for how to do it. You'll need to do several things:

(i) Verify that lies on the line . You can do this easily by showing that there exists some such that when you plug into it generates .

(ii) You will need to verify that is perpendicular to the direction vector of the line . This is done by using the dot product and showing it becomes 0.

(iii) You will need to verify that is perpendicular to the direction vector of the line parallel to , but passing through the point . However, if you've done part (ii), there is absolutely no need to do this part since the lines are parallel and hence they have the same direction vectors.

(iv) You then need to conclude by saying that since AB is perpendicular to both lines, and A is the foot of the perpendicular, then B must be the other foot of the perpendicular.
5. (Original post by Zacken)
As for how to do it. You'll need to do several things:

(i) Verify that lies on the line . You can do this easily by showing that there exists some such that when you plug into it generates .

(ii) You will need to verify that is perpendicular to the direction vector of the line . This is done by using the dot product and showing it becomes 0.

(iii) You will need to verify that is perpendicular to the direction vector of the line parallel to , but passing through the point . However, if you've done part (ii), there is absolutely no need to do this part since the lines are parallel and hence they have the same direction vectors.

(iv) You then need to conclude by saying that since AB is perpendicular to both lines, and A is the foot of the perpendicular, then B must be the other foot of the perpendicular.
Thank you so much, Zacken! I really appreciate it
6. (Original post by Phoebus Apollo)
Thank you so much, Zacken! I really appreciate it
No problem, sorry for the late reply.

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