Date | May 2021 | Marks available | 3 | Reference code | 21M.1.AHL.TZ1.13 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Find | Question number | 13 | Adapted from | N/A |
Question
A submarine is located in a sea at coordinates (0.8, 1.3, −0.3) relative to a ship positioned at the origin O. The x direction is due east, the y direction is due north and the z direction is vertically upwards.
All distances are measured in kilometres.
The submarine travels with direction vector (-2-31).
The submarine reaches the surface of the sea at the point P.
Assuming the submarine travels in a straight line, write down an equation for the line along which it travels.
Find the coordinates of P.
Find OP.
Markscheme
r=(0.81.3-0.3)+λ(-2-31) A1A1
Note: Award A1 for each correct vector. Award A0A1 if their “r=” is omitted.
[2 marks]
-0.3+λ=0 (M1)
⇒λ=0.3
r=(0.81.3-0.3)+0.3(-2-31)=(0.20.40) (M1)
P has coordinates (0.2, 0.4, 0) A1
Note: Accept the coordinates of P in vector form.
[3 marks]
√0.22+0.42 (M1)
=0.447 km (=447 A1
[2 marks]