Exercises for Question Type 1: Finding the point of intersection for a line and a plane

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Exercises for Question Type 1: Finding the point of intersection for a line and a plane - IB

Question 1

Determine the point of intersection of the line (x, y, z) = (2, 3, 4) + t (- 1, 0, 2) with the plane 4 x - y + z = 10 .

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Question 2

Determine the point where the line (x, y, z) = (- 3, 2, 1) + t (7, - 5, 4) intersects the plane 3 x - y + 2 z = 8 .

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Question 3

Find the intersection of the line (x, y, z) = (2, 0, - 1) + t (0, 5, 2) with the plane 2 x - 3 y + z = 4 .

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Question 4

Find the coordinates of the point where the line (x, y, z) = (5, - 2, 1) + t (3, 1, - 4) meets the plane 6 x + 2 y - 3 z = 7 .

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Question 5

Compute the intersection of the line (x, y, z) = (1, 0, 3) + t (- 2, 2, 1) with the plane 5 x + y - 2 z = 9 .

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Question 6

Find the point of intersection of the line (x, y, z) = (0, 1, - 2) + t (3, - 2, 4) with the plane x - 4 y + 2 z = 5 .

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Question 7

Find the point of intersection of the line given by x y z = 321 + t 141 with the plane 2 x + 6 y + z = 1 .

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Question 8

Find the coordinates of the point of intersection of the line r = 1 - 1 2 + t 213 with the plane x + 2 y - 3 z = 4 .

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Question 9

Find the coordinates of the intersection of the line with equation r = t 12 - 1 and the plane with equation 3 x - y + 2 z = 5 .

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Question 10

Where does the line x y z = 111 + t 111 intersect the plane x + y + z = 6 ?

Question 11

Determine where the line (x, y, z) = (- 2, 3, 5) + t (4, - 1, - 2) meets the plane - x + 2 y + 3 z = 1 .

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Question 12

Compute the intersection of the line (x, y, z) = (- 1, 4, 3) + t (2, - 3, 1) with the plane x - y + 4 z = 2 .

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IB Mathematics Analysis and Approaches Question Type 1: Finding the Point of Intersection for a Line and a Plane Exercises