Question 11:
11 | Obtains a position vector
of a point on L .
1 | AO2.5 | B1 |  2   3   2  12
       
r = −4 +µ 8 = −4 +µ 32
1        
       
5 4 5 4 5 4  5 
−2 2
   
r = 0 +λ 1
2    
   
 3  3
 2  −2  4 
     
−4 − 0 = −4
     
     
5 4  3   −7 4
12 2  91 
     
32 × 1 = −26
     
     
 5  3  −52
4
91
−4
� �.�−26�
7
− −52 43
4
=
1 3 √ 6 9 =√56.197659...=5.18 3sf
Obtains a direction vector
for L
1
ISW | AO1.1b | B1
Obtains a position vector
of a point on L and a
2
direction vector for L
2 | AO2.5 | B1
Obtains a correct vector
between the two lines.
Follow through from their
position vectors | AO1.1b | B1F
Calculates the vector
product of their two
direction vectors
or
calculates the scalar
product of the general
vector between the lines
with both direction
vectors to obtain a pair of
simultaneous equations | AO3.1a | M1
Obtains the correct vector
product
or
obtains a correct pair of
simultaneous equations | AO1.1b | A1
Uses their vector product
or the solutions to their
simultaneous equations
to calculate the shortest
distance between the two
lines | AO3.1a | M1
Obtains the correct
shortest distance.
Allow awrt 5.18
Accept exact answer | AO1.1b | A1
Total | 8
Q | Marking Instructions | AO | Marks | Typical Solution