Question

Determine the point of intersecting of the 2 lines

⟨x,y,z⟩=⟨4,2,4⟩+⟨2,2,1⟩t and

⟨x,y,z⟩=⟨-5,2,-8 ⟩+⟨ 20,8,20⟩s

( Blank 1. Calculate the answer by read surrounding text.

, Blank 2. Calculate the answer by read surrounding text.

, Blank 3. Calculate the answer by read surrounding text.

)

Answer 1

$4+2t=-5+20s$ ......(i)

$2+2t=2+8s.....(ii)$

$(i)-(ii)$

$2=-7+12s$

$s=\frac{3}{4}$

From $(i)$

$2t=-9+20(\frac{3}{4})$

$t=3$

Point of intersection

$4+2(3)=10\\ 2+2(3)=8\\4+3=7$

$(10,8,7)$