ligilleering 1. MC04500 Mathematics for Engineering . T1-2018 12 March-18 March

Question

ligilleering 1. MC04500 Mathematics for Engineering . T1-2018 12 March-18 March > week 4 Quiz The line L1 has an equation r1- +n and the line L2 has an equation T2 = +m Different values of n give different points on line L1 Similarly, different values of m give different points on line L2- If the two lines intersect then r1 = r2 at the point of intersection. If you can find values of n and m this condition then the two lines intersect Show the lines intersect by finding these values n and m hence find the point of intersection. n=? Answer: Next page age r your research and study only. Further reproduction, transmission or sale without permission is prohibited. - Disclaimer and copyright - Privacy - Monash College CRICOS Provider Number: 01857J 22:43 You are logged in as Minghan Shan (Log out) ip

Explanation / Answer

Solution:

r1=r2 gives,

<6, 4, 11> + n<4, 2, 9> = <-3, 10, 2> + m<-5, 8, 0>

implies, <6, 4, 11> - <-3, 10, 2> = m<-5, 8, 0> - n<4, 2, 9>

implies,<9, -6, 9> = <-5m-4n, 8m-2n, -9n>

Conparing each entry if the vectors in both sides we get,

-5m - 4n= 9 ----- (i)

8m - 2n = -6 ----- (ii)

- 9n = 9 ----- (iii)

Now (iii) gives, n = -1.

(ii) gives, 8m = -6 + 2n

i.e, 8m = -6 + 2(-1) i.e, 8m = -6-2

i.e, 8m = -8 i.e, m = -1

Put n=-1 in r1 or m=-1 in r2 to get the intersection point.

Putting n=-1 in r1 we get the intersection poit p.

p =  <6,4,11> + (-1)<4,2,9> = <6, 4, 11> - <4, 2, 9> = <6-4, 4-2, 11-9> = <2, 2, 2>

The point of intersection is <2, 2, 2>

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.