| Date | None Specimen | Marks available | 1 | Reference code | SPNone.2.sl.TZ0.4 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Write down | Question number | 4 | Adapted from | N/A |
Question
Consider the lines L1L1 , L2L2 , L2L2 , and L4L4 , with respective equations.
L1L1 : (xyz)=(123)+t(3−21)⎛⎜⎝xyz⎞⎟⎠=⎛⎜⎝123⎞⎟⎠+t⎛⎜⎝3−21⎞⎟⎠
L2L2 : (xyz)=(123)+p(321)⎛⎜⎝xyz⎞⎟⎠=⎛⎜⎝123⎞⎟⎠+p⎛⎜⎝321⎞⎟⎠
L3L3 : (xyz)=(010)+s(−12−a)⎛⎜⎝xyz⎞⎟⎠=⎛⎜⎝010⎞⎟⎠+s⎛⎜⎝−12−a⎞⎟⎠
L4L4 : (xyz)=q(−64−2)⎛⎜⎝xyz⎞⎟⎠=q⎛⎜⎝−64−2⎞⎟⎠
Write down the line that is parallel to L4L4 .
[1]
a.
Write down the position vector of the point of intersection of L1L1 and L2L2 .
[1]
b.
Given that L1L1 is perpendicular to L3L3 , find the value of a .
[5]
c.
Markscheme
L1L1 A1 N1
[1 mark]
a.
(123)⎛⎜⎝123⎞⎟⎠ A1 N1
[1 mark]
b.
choosing correct direction vectors A1A1
e.g. (3−21)⎛⎜⎝3−21⎞⎟⎠ , (−12−a)⎛⎜⎝−12−a⎞⎟⎠
recognizing that a∙b=0 M1
correct substitution A1
e.g. −3−4−a=0
a=−7 A1 N3
[5 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
