Exercises for Question Type 2: Given 2 vectors, classifying what type of lines they are

Exercises for Question Type 2: Given 2 vectors, classifying what type of lines they are - IB

Written by official IB examiners

Question 1

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by:

$L_{1} : r = 000 + t 111$

$L_{2} : r = 123 + s 124$

[6]

Question 2

Skill question

Classify the relationship between the lines $L_{1} : (1, 1, 1) + t (3, 6, 9)$ and $L_{2} : (4, 7, 10) + s (1, 2, 3)$ .

[5]

Question 3

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by: $L_{1} : r = 111 + t 2 - 1 3$ $L_{2} : r = 304 + s - 1 2 - 2$

[6]

Question 4

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by:

$L_{1} : r = 000 + t 110$

$L_{2} : r = 011 + s 101$

[7]

Question 5

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by:

$L_{1} : r = 210 + t 420$

$L_{2} : r = 135 + s 210$

[4]

Question 6

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by: $L_{1} : r = 123 + t 246$ $L_{2} : r = 010 + s 123$

Classify the relationship between the lines.

[5]

Question 7

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by: $L_{1} : r = 2 - 1 3 + t 42 - 6$ $L_{2} : r = 61 - 3 + s 21 - 3$

[5]

Question 8

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by:

$L_{1} : r = 101 + t 234$

$L_{2} : r = 259 + s 468$

[6]

Question 9

Skill question

Classify the relationship between the lines $L_{1} : r = 111 + t 123$ and $L_{2} : r = 503 + s 4 - 1 2$ .

[7]

Question 10

Skill question

Classify the relationship between the lines $L_{1} : r = 123 + t 101$ and $L_{2} : r = 224 + s 01 - 1$ .

[6]

Question 11

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by: $L_{1} : r = 301 + t 112$ $L_{2} : r = 123 + s 2 - 1 1$

[6]

Question 12

Skill question

Classify the relationship between the lines $L_{1}$ and $L_{2}$ defined by:

$L_{1} : r = 012 + t 3 - 1 2$

$L_{2} : r = 6 - 1 6 + s 3 - 1 2$

[5]

IB Mathematics Analysis and Approaches Question Type 2: Given 2 Vectors, Classifying What Type of Lines They Are Exercises