Exercises for Question Type 1: Finding the point of intersection for two lines

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Exercises for Question Type 1: Finding the point of intersection for two lines - IB

Question 1

Find the coordinates of the point of intersection of the lines L_{1} and L_{2} defined by the equations: L_{1} : r = - 2 13 + t 4 - 3 2 L_{2} : r = 4 - 7 8 + u - 2 5 - 3

[6]

Question 2

Find the point of intersection of the lines L_{1} and L_{2} defined by: L_{1} : r = 102 + t 21 - 1 L_{2} : r = 11 - 1 + u 101

[5]

Question 3

Determine the coordinates of the intersection of the lines L_{1} and L_{2} defined by: L_{1} : r = 230 + t 3 - 2 1 L_{2} : r = 12 - 7 1 + u - 1 42

[6]

Question 4

Find the coordinates of the point of intersection of the lines L_{1} and L_{2} defined by the following equations: L_{1} : r = 013 + t 12 - 1 L_{2} : r = 442 + u 2 - 1 1

[6]

Question 5

Determine the coordinates of the intersection of the lines L_{1} and L_{2} : L_{1} : r = (1, 1, 1) + t (5, 2, - 1) L_{2} : r = (2, 17, - 7) + u (3, - 4, 2)

[6]

Question 6

Determine the coordinates of the point of intersection of the following two lines: L_{1} : r = 210 + t 3 - 1 2 L_{2} : r = 5 - 2 4.5 + u 11 - 1

[5]

Question 7

Calculate the intersection point of the lines: L_{1} : r L_{2} : r = 123 + t 0.5 1 - 1 = 1.5 6.75 - 4 + u 1 - 0.5 2

Find the coordinates of the intersection point.

[6]

Question 8

The lines L_{1} and L_{2} are defined by: L_{1} : r = 012 + t 234 L_{2} : r = 1.25 1.25 4.5 + u - 1 5 - 2

Find the coordinates of the point of intersection of the two lines.

[6]

Question 9

Find the intersection point of the lines: L_{1} : r = 000 + t 123, L_{2} : r = 345 + u - 2 - 3 - 4

[6]

Question 10

Find the coordinates of the point of intersection of the lines L_{1} and L_{2} . L_{1} : r = 001 + t 123 L_{2} : r = 2.5 3.5 6 + u 211

[6]

Question 11

Calculate the intersection point of L_{1} : (- 1, 0, 4) + t (2, 1, 3), L_{2} : (- 1, - 1, 9) + u (1, 1, - 1) .

[6]

IB Mathematics Analysis and Approaches Question Type 1: Finding the Point of Intersection for Two Lines Exercises