5. Three waka ama teams are on the uta (shore) waiting to race. These teams are imaginatively named A, B and C. Their starting positions are labeled on the graph below. 6 4 2 A 2 D B 6 8 C 10 (a) What is the vector equation of the line team A must follow to get to point D in the bay? (b) What are the parametric equations of the line team B must follow to get to point D? (c) What is the angle between the two lines in (a) and (b)?

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Three waka ama teams are on the uta (shore) waiting to race. These teams are imaginatively

named A, B and C. Their starting positions are labeled on the graph below.

5. Three waka ama teams are on the uta (shore) waiting to race. These teams are imaginatively
named A, B and C. Their starting positions are labeled on the graph below.
D.
6
4-
2-
6
8
10
(a) What is the vector equation of the line team A must follow to get to point D in the bay?
(b) What are the parametric equations of the line team B must follow to get to point D?
(c) What is the angle between the two lines in (a) and (b)?
(d) Team B realises that they will crash into Team A if they follow the line in (b), so instead
they decide to follow a line which is parallel to A. What is the vector equation of the
line they are following now (assuming they are starting from the beach again)?
(e) What is the vector equation of the line team C must follow if they wish to meet team A
at right angles?
(f) If team C follows the line in part (e), at what point will it meet the line that team A
took?
(g) Show that the direction vector for Team C (from (e)) can be written as a linear combi-
nation of the direction vectors for Teams A and B (from (a) and (b)).
2.
Transcribed Image Text:5. Three waka ama teams are on the uta (shore) waiting to race. These teams are imaginatively named A, B and C. Their starting positions are labeled on the graph below. D. 6 4- 2- 6 8 10 (a) What is the vector equation of the line team A must follow to get to point D in the bay? (b) What are the parametric equations of the line team B must follow to get to point D? (c) What is the angle between the two lines in (a) and (b)? (d) Team B realises that they will crash into Team A if they follow the line in (b), so instead they decide to follow a line which is parallel to A. What is the vector equation of the line they are following now (assuming they are starting from the beach again)? (e) What is the vector equation of the line team C must follow if they wish to meet team A at right angles? (f) If team C follows the line in part (e), at what point will it meet the line that team A took? (g) Show that the direction vector for Team C (from (e)) can be written as a linear combi- nation of the direction vectors for Teams A and B (from (a) and (b)). 2.
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