Name: ________________________________
Date: _______________
VECTOR PROBLEM SET
What’s on the Test?
⃗⃗⃗⃗⃗ )
 Find a vector (i.e. 𝑃𝑄
 Writing the equation of a vector
 Finding the angle between two vectors
 Finding the magnitude or speed of a vector
 Finding a coordinate using a vector equation
 Identifying and finding parallel and perpendicular vectors
⃗⃗⃗⃗⃗ )
 Position vectors (i.e. given point B, its position vector would be 𝑂𝐵
 Finding the point of intersection given two vector equations
 Using a vector equation to determine if a point lies on it
1.
2.
3.
4.
5.
Points A, B, and C have position vectors 4i + 2j, i – 3j and – 5i – 5j. Let D be a point on the x-axis
such that ABCD forms a parallelogram.
(a)
(i)
Find BC .
(ii)
Find the position vector of D.
(4)
(b)
Find the angle between BD and AC .
(6)
The line L1 passes through A and is parallel to i + 4j. The line L2 passes through B and is parallel to
2i + 7j. A vector equation of L1 is r = (4i + 2j) + s(i + 4j).
(c)
Write down a vector equation of L2 in the form r = b + tq.
(1)
(d)
The lines L1 and L2 intersect at the point P. Find the position vector of P.
(4)
(Total 15 marks)
6. The following diagram shows a solid figure ABCDEFGH. Each of the six faces is a parallelogram.
The coordinates of A and B are A (7, –3, –5), B(17, 2, 5).
(a)
Find
(i)
AB;
(ii)
AB .
(4)
The following information is given.
  6
  2
 
 
AD =  6  , AD = 9, AE =   4  , AE = 6
 3 
 4 
 
 
(b)
(i)
Calculate AD • AE .
(ii)
Calculate AB • AD .
(iii)
Calculate AB • AE .
(iv)
Hence, write down the size of the angle between any two intersecting edges.
(5)
(c)
Calculate the volume of the solid ABCDEFGH.
(2)
(d)
The coordinates of G are (9, 4, 12). Find the coordinates of H.
(3)
(e)
The lines (AG) and (HB) intersect at the point P.
2
 
Given that AG =  7  , find the acute angle at P.
17 
 
(5)
(Total 19 marks)