(C4) I've been stuck on this vector question for an hour? :(Watch
It's question 5b)
I just don't get it
Can you post your attempt at the solution?
r= (6+l)i + (19+4l)j + (-1-1l)k
If two vectors are perpendicular, their dot product is 0.
Now you want to find the vector OP. Well we are told it is on the line l, thus we can just say the vector OP is:
(x,y,z) = (6,19,-1) + lambda (1,4,-2) for some lambda. Your objective now is to find lambda?
So you now have equations for x,y and z, write them out. Also, you have the condition that (x,y,z) and (1,4,-2) are perpendicular. Thus solve the simultaneous equations for lambda. What do you get?
P must be on the line L1. So P must have coordinates (6+l)i + (19+4l)j + (-1-2l)k, for some particular value of l (which you are trying to find out)
O (The origin) has coordinates 0i +0j + 0k
So the direction vector of OP is (6+l)i + (19+4l)j + (-1-2l)k - 0i +0j + 0k
=(6+l)i + (19+4l)j + (-1-2l)k
Now you have a and b