Question

1a). In three-space, find the intersection point of the two lines: (x, y, z) = (-1,2,0] + [3,-1, 4) and [x, y, ) = -6, 8, -1] + [2,-5, -3). b) Determine a direction vector in integer form of the line of intersection of the two planes 2x + 2y+2-12-0 and (x, y, z)=(2,0,0]+${1,2,0]+(1.0,-2) [2,3] 2. What is the distance between the point (-81) and the plane 5x-2-2y+52 [2] 3. Find the point(s) of intersection for the following three planes. T: x-y +z = 0 : x +2y-2-8=0 Tg: 2x - 2y +z+11=0

vectors. Need help with those questions please

Answer 1

The are a given equation of the lines re (2,7, 8) = (-1,2,0) +413,-1,4) and czy, o = (-6,8,-1) + s( 2,-5,-). __@) at IP(-1+3f, 2-t, at be the point 7 inforsetion of the lines as andes since this point lies on (2), we have -173t = - 6+28 in 543t =25 art =8-55 4ta-1-35 47+/ 32- atplott 5 3 20145 -18-36 in 28t 2-23 ig t=1 Therefor ine point of intersection isp/-1, 3, -4)

(6) we first convert the plane con [2, a - [+, 0,07 + 3 [1,20] + + [1,0,-2) in general covation. we write alt set= x - £. - insai z = 2t i r = - 2 from " ² - 2 = -2 or 2n-1 = yet og 27-y+tala (2) ut l, min the the direction vector of the line of intersection of the plane (2) and 2n+2y +27-1220 so we have. al-mino. al+20+20=0 1-2 2- ** 2. 4+2 . iny 2 2 2 2 2 2 2 3 in the direction veltor as (2,1,-3)

I (2) point 14, -8,1) the and distance the plane between the 54-2=27th in 50-27-2-920 is 5.4 -2.(-8) – (40) -5) Nonito 55+ (-2) p (+1) nde 1204167-5) V 25+41) 30 Bo RS 2730