Exercises for Question Type 3: Finding the intersection of three planes

Question 1

Skill question

Determine the intersection point of the planes $x - 2 y + z = 1$ , $3 x + y - z = 4$ , and $2 x - y + 2 z = 5$ .

[7]

Question 2

Skill question

Solve for the intersection of the planes $3 x + 2 y - z = 4$ , $2 x - y + 4 z = 5$ , and $x + 3 y + z = 6$ .

[10]

Question 3

Skill question

Solve for the common point of the planes: $2 x + 3 y - z x - y + 2 z 4 x + y + z = 5 = 3 = 9$

[7]

Question 4

Skill question

Determine the intersection of the planes $5 x - 2 y + z = 3$ , $x + y - 3 z = - 2$ , and $2 x - y + 4 z = 7$ .

[7]

Question 5

Skill question

Find the point where the planes $x + 2 y + 3 z = 13$ , $2 x - y + z = 3$ , and $3 x + y - 2 z = - 1$ intersect.

[8]

Question 6

Skill question

Solve for the unique intersection of the following system of equations: $x + y + z 2 x + 3 y + 4 z 3 x - 2 y + z = 1 = 4 = 2$

[5]

Question 7

Skill question

Find the intersection point of the planes $x + y + z = 6$ , $2 x - y + 3 z = 14$ , and $- x + 4 y + z = 2$ .

[10]

Question 8

Skill question

Find the intersection point of the planes $4 x - y + 2 z = 6$ , $- x + 2 y - 3 z = - 4$ , and $3 x + y + z = 8$ .

[6]

Question 9

Skill question

Solve for the intersection of the planes $x - y + 2 z = 0$ , $2 x + 3 y - z = 9$ , and $- 3 x + y + 4 z = 5$ .

[8]

Question 10

Skill question

Find the intersection of the planes $3 x - 2 y + z = 1$ , $x + y - 4 z = 2$ , and $2 x - 3 y + 5 z = 3$ .

[6]

Question 11

Skill question

Find the common point of the planes $4 x + y - z = 8$ , $- 2 x + 3 y + 2 z = 1$ , and $x + y + z = 6$ .

[7]

Question 12

Skill question

Find the unique solution of the system given by $2 x - y + 3 z = 4$ , $- x + 4 y - z = - 5$ , and $3 x + y + 2 z = 7$ .

[7]

IB Mathematics Analysis and Approaches Question Type 3: Finding the Intersection of Three Planes Exercises