Date | May 2019 | Marks available | 6 | Reference code | 19M.2.SL.TZ2.S_7 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Find | Question number | S_7 | Adapted from | N/A |
Question
The vector equation of line is given by r .
Point P is the point on that is closest to the origin. Find the coordinates of P.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
METHOD 1 (Distance between the origin and P)
correct position vector for OP (A1)
eg ,
correct expression for OP or OP2 (seen anywhere) A1
eg ,
valid attempt to find the minimum of OP (M1)
eg , root on sketch of , min indicated on sketch of
(A1)
substitute their value of into (only award if there is working to find ) (M1)
eg one correct coordinate,
A1 N2
METHOD 2 (Perpendicular vectors)
recognizing that closest implies perpendicular (M1)
eg (may be seen on sketch),
valid approach involving (M1)
eg
correct scalar product A1
eg , ,
(A1)
substitute their value of into or (only award if scalar product used to find ) (M1)
eg one correct coordinate,
A1 N2
[6 marks]