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## 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

__4__and

**i**+3**j**-**k**__respectively.__

**i**+4**j**+4**k**(a) Find the vector equation of the line l

_{1}which passes through A and B.

The line l

_{2}has equation

**r**=22

**i**+a

**j**+4

**k**+μ(b

**i**-

**j**+2

**k**), where μ is scalar parameter and a and b are constants.

The lines l

_{1}and l

_{2}are perpendicular and intersect. Find:

(b) the values of a and b

(c) the position vector of the point of intersection of l

_{1}and l

_{2}

## 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

**4.Conclusion**

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

Regards,

-A

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