8:33 msr02.math.mcgill.ca all Fido 6: Problem 13 Previous Problem List Next (1 p

Question

8:33 msr02.math.mcgill.ca all Fido 6: Problem 13 Previous Problem List Next (1 point) Find points PQ which are closest possible with P lying on the line x=-6 + lt, y = 0-7, z = 7-16t and Q lying on the line x = 451 + 7, y = 10 13-71, z =-243-8. Hint: Use the fact that the line joining P and Q is perpendicular to the two given lines Q=( Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0%. You have unlimited attempts remaining. Email instructor

Explanation / Answer

perpendicular to line r(t) = {-6,0,7} + t {1,-7,-16}
2(x - x) + 3(y - y) + 9(z - z) = 0
1((-6+1t) - (451+7s)) -7((0-7t) - (1013-7s)) -16((7-16t) - (-243-8s)) = 0
simplify that gives
-184s+306t+2634=0...(i)

.... perpendicular to line r(s) = {451,1013,-243) + s {7,-7,-8}
7(x - x) -7(y - y) -8(z - z) = 0
7((-6+1t) - (451+7s)) -7((0-7t) - (1013-7s)) -8((7-16t) - (-243-8s)) = 0
simplify that gives
-162s+184t+1892=0
184t=162s-1892
t=(162s-1892)/184...(ii)

Now plug (ii) into (i)
-184s+306t+2634=0
-184s+306[(162s-1892)/184]+2634=0
simplifying that gives
s=6
now plug s=6 into (ii)
t=(162s-1892)/184=(162*6-1892)/184=-5

Now plug t=-5 into x=-6+1t, y=0-7t, z=7-16t
we get x=-11, y=35, z=87
Hence point P is (-11, 35, 87)

Now plug s=6 into x=451+7s, y=1013-7s, z=-243-8s
we get x=493, y=971, z=-291
Hence point Q is (493, 971, -291)

Related Questions

Navigate

• Browse (All)
• Browse 8
• Subjects

---

---

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