Vector Equations for Perpendicular Lines: Finding Intersection Point

[arianabedi]

Homework Statement

This is a "exam style" question for A-Level mathematics regarding vectors. The question is as followed:

Relative to a fixed origin O, the points A and B have position vectors 4i+3j-k and i+4j+4k respectively.

(a) Find the vector equation of the line l₁ which passes through A and B.

The line l₂ has equation r=22i+aj+4k+μ(bi-j+2k), where μ is scalar parameter and a and b are constants.
The lines l₁ and l₂ are perpendicular and intersect. Find:

(b) the values of a and b

(c) the position vector of the point of intersection of l₁ and l₂

Homework Equations

Vector equation of a strait line through two points C and D:

r=c+t(d-c)

if there is any other ones, I am unfortunately unaware of

The Attempt at a Solution

Sadly I've been given no knowledge of how to do this question since vectors is not a part of my course. Therefore there are no attempts made4.Conclusion
This question is really getting into my head and any help would be greatly appreciated.

Regards,
-A

 

[Mark44]

Homework Statement

This is a "exam style" question for A-Level mathematics regarding vectors. The question is as followed:

Relative to a fixed origin O, the points A and B have position vectors 4i+3j-k and i+4j+4k respectively.

(a) Find the vector equation of the line l₁ which passes through A and B.

The line l₂ has equation r=22i+aj+4k+μ(bi-j+2k), where μ is scalar parameter and a and b are constants.
The lines l₁ and l₂ are perpendicular and intersect. Find:

(b) the values of a and b

(c) the position vector of the point of intersection of l₁ and l₂

Homework Equations

Vector equation of a strait line through two points C and D:

r=c+t(d-c)

if there is any other ones, I am unfortunately unaware of

The Attempt at a Solution

Sadly I've been given no knowledge of how to do this question since vectors is not a part of my course. Therefore there are no attempts made

Then why don't you wait until vectors are presented in your course, or when you take a course where vectors are presented?

4.Conclusion
This question is really getting into my head and any help would be greatly appreciated.

Regards,
-A

 

[arianabedi]

Then why don't you wait until vectors are presented in your course, or when you take a course where vectors are presented?

Well the reason is that I've been told by my tutor that I will not be studying vectors.

 

[Mark44]

Then how do you expect to be able to solve problems that involve vectors?

 

[HallsofIvy]

For this problem, all you really need to know is that a point with position vector ai+ bj+ ck has coordinates (a, b, c).