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Created by T. Madas




VECTOR
EXAM
QUESTIONS
Part A




Created by T. Madas

, Created by T. Madas

Question 1 (**)
The straight line l1 passes through the points with coordinates ( 5,1,6 ) and ( 2, 2,1) .


a) Find a vector equation of l1 .


A different straight line l2 passes though the point C ( 6, 6, −4 ) and is parallel to the
vector 4i − 2 j + 3k .

b) Show clearly that l1 and l2 are skew.


FP1-K , r = 5i + j + 6k + λ ( 3i − j + 5k )




Created by T. Madas

, Created by T. Madas

Question 2 (**)
Relative to a fixed origin O , the respective position vectors of three points A , B and
C are

 3  −5   4
     
 2,  11 and  0  .
9  6  −8 
     








a) Determine, in component form, the vectors AB and AC .

b) Hence find, to the nearest degree, the angle BAC .

c) Calculate the area of the triangle BAC .








AB = −8i + 9 j − 3k , AC = i − 2 j − 17k , θ ≈ 83° , area ≈ 106




Created by T. Madas

, Created by T. Madas

Question 3 (**)
The straight line l1 passes through the points A ( 2,5,9 ) and B ( 6, 0,10 ) .


a) Find a vector equation for l1 .


The straight line l2 has vector equation


8  2
   
r = 8 + µ  1 ,
0  −3 
   

where µ is a scalar parameter.

b) Show that the point A is the intersection of l1 and l2 .


c) Show further that l1 and l2 are perpendicular to each other.


r = 2i + 5 j + 9k + λ ( 4i − 5 j + k )




Created by T. Madas