Find the vectorequation of the linex=-8-t,y=11-3t,z=-1-4tthrough the point(4,5,5) that meets theline at right angles.Determine a vectorequation of a linethat goes throughthe points 𝐴(1,4)and 𝐡(3,1)Β Β determine if the lines areintersect or are parallel,coincident, or skew. If theyintersect, find the point ofintersection.Β R1 = (2,1,0) + s(1,βˆ’1,1)R2= (3,0,βˆ’1) + t(2,3,βˆ’1)Find the anglethat the line 3x+ 8y βˆ’ 12 = 0οΏ½makes withthe x-axis.Β Determine theintersection of thefollowing pairs of linesif it existsΒ L1: x + 3y + 10=0L2: 2x βˆ’ 9y + 5=0Β Β Β Find the distancebetween each of thefollowing pairs ofparallel lines.Β L1: (5,2,3) + s(2,1,2)L2: (βˆ’4,2,4) + t(2,1,2)Explain whylines havescalarequations inR2, but not R3.Determine the scalarequation The lineperpendicular to thevector (3,2) thatpasses through thepoint(2,-6) .Find the anglebetween each pairof lines.L1: (16,12) + t(2,3)L2: (15,βˆ’4) +s(7,βˆ’1)6. Find the distancebetween each of thefollowing pairs ofskew linesL1: (4,1,0) + s(1,3,2)L2: (βˆ’5,3,3) +t(βˆ’1,1,2)Determine thedistance fromthe point P(3,5) to the line2x βˆ’ y + 7 = 0.Determine theangle between thepair of lines.L1 :(4,5,βˆ’2) +t(3,βˆ’1,βˆ’1)L2 : (4,5,βˆ’2) +s(βˆ’2,βˆ’3,2)5. If the points(8,4,14),(6,19,βˆ’4)(10, b, c) lie on thesame straight line,find the values of band cFree!Determine if the twogiven equationsrepresent twodifferent lines or thesame line.: (7,2) + t(2,1): (4,5) + s(4,2)Given the line ,determine if thefollowing line isparallel, perpendicular,or coincident to it.L1: (2,βˆ’3,8) + t(2,1,2)L2; x = 1 + 2ty = 21 βˆ’ 1tz = 7 βˆ’ 2tΒ Find the vectorequation of the linex=-8-t,y=11-3t,z=-1-4tthrough the point(4,5,5) that meets theline at right angles.Determine a vectorequation of a linethat goes throughthe points 𝐴(1,4)and 𝐡(3,1)Β Β determine if the lines areintersect or are parallel,coincident, or skew. If theyintersect, find the point ofintersection.Β R1 = (2,1,0) + s(1,βˆ’1,1)R2= (3,0,βˆ’1) + t(2,3,βˆ’1)Find the anglethat the line 3x+ 8y βˆ’ 12 = 0οΏ½makes withthe x-axis.Β Determine theintersection of thefollowing pairs of linesif it existsΒ L1: x + 3y + 10=0L2: 2x βˆ’ 9y + 5=0Β Β Β Find the distancebetween each of thefollowing pairs ofparallel lines.Β L1: (5,2,3) + s(2,1,2)L2: (βˆ’4,2,4) + t(2,1,2)Explain whylines havescalarequations inR2, but not R3.Determine the scalarequation The lineperpendicular to thevector (3,2) thatpasses through thepoint(2,-6) .Find the anglebetween each pairof lines.L1: (16,12) + t(2,3)L2: (15,βˆ’4) +s(7,βˆ’1)6. Find the distancebetween each of thefollowing pairs ofskew linesL1: (4,1,0) + s(1,3,2)L2: (βˆ’5,3,3) +t(βˆ’1,1,2)Determine thedistance fromthe point P(3,5) to the line2x βˆ’ y + 7 = 0.Determine theangle between thepair of lines.L1 :(4,5,βˆ’2) +t(3,βˆ’1,βˆ’1)L2 : (4,5,βˆ’2) +s(βˆ’2,βˆ’3,2)5. If the points(8,4,14),(6,19,βˆ’4)(10, b, c) lie on thesame straight line,find the values of band cFree!Determine if the twogiven equationsrepresent twodifferent lines or thesame line.: (7,2) + t(2,1): (4,5) + s(4,2)Given the line ,determine if thefollowing line isparallel, perpendicular,or coincident to it.L1: (2,βˆ’3,8) + t(2,1,2)L2; x = 1 + 2ty = 21 βˆ’ 1tz = 7 βˆ’ 2tΒ 

Unit 6 - Equations and Intersections of Lines - Call List

(Print) Use this randomly generated list as your call list when playing the game. Place some kind of mark (like an X, a checkmark, a dot, tally mark, etc) on each cell as you announce it, to keep track. You can also cut out each item, place them in a bag and pull words from the bag.


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  1. A- Find the vector equation of the line x=-8-t,y=11-3t,z=-1-4t through the point (4,5,5) that meets the line at right angles.
  2. M-Determine a vector equation of a line that goes through the points 𝐴(1,4) and 𝐡(3,1)
  3. H-determine if the lines are intersect or are parallel, coincident, or skew. If they intersect, find the point of intersection. R1 = (2,1,0) + s(1,βˆ’1,1) R2= (3,0,βˆ’1) + t(2,3,βˆ’1)
  4. H-Find the angle that the line 3x + 8y βˆ’ 12 = 0 οΏ½makes with the x-axis.
  5. H-Determine the intersection of the following pairs of lines if it exists L1: x + 3y + 10=0 L2: 2x βˆ’ 9y + 5=0
  6. M-Find the distance between each of the following pairs of parallel lines. L1: (5,2,3) + s(2,1,2) L2: (βˆ’4,2,4) + t(2,1,2)
  7. T-Explain why lines have scalar equations in R2, but not R3.
  8. A-Determine the scalar equation The line perpendicular to the vector (3,2) that passes through the point(2,-6) .
  9. A-Find the angle between each pair of lines. L1: (16,12) + t(2,3) L2: (15,βˆ’4) + s(7,βˆ’1)
  10. T-6. Find the distance between each of the following pairs of skew lines L1: (4,1,0) + s(1,3,2) L2: (βˆ’5,3,3) + t(βˆ’1,1,2)
  11. T-Determine the distance from the point P(3, 5) to the line 2x βˆ’ y + 7 = 0.
  12. M-Determine the angle between the pair of lines. L1 :(4,5,βˆ’2) + t(3,βˆ’1,βˆ’1) L2 : (4,5,βˆ’2) + s(βˆ’2,βˆ’3,2)
  13. T-5. If the points (8,4,14),(6,19,βˆ’4) (10, b, c) lie on the same straight line, find the values of b and c
  14. A-Free!
  15. M-Determine if the two given equations represent two different lines or the same line. : (7,2) + t(2,1) : (4,5) + s(4,2)
  16. H-Given the line , determine if the following line is parallel, perpendicular, or coincident to it. L1: (2,βˆ’3,8) + t(2,1,2) L2; x = 1 + 2t y = 21 βˆ’ 1t z = 7 βˆ’ 2t