K
Higher Homework 3
N
Section 1: Vectors
1. PQRS,KLMN is a cuboid as shown in the diagram.
SN  u, SR  v and SP  w. T is the midpoint of KR.
L
M
u
a) Express KT in terms of u, v and w.
b) If |𝑢| = √2, |𝑤| = 2 𝑎𝑛𝑑 |𝑣 | = 5, find the value of u.(u + w – v)
T
w
P
S
v
Section 2: Preparation for assessment of Vectors(E1.4)
2
−2
⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗
2.
The vectors 𝐴𝐵𝑎𝑛𝑑𝐴𝑄 are given by 𝐴𝐵 = (−3) 𝑎𝑛𝑑 𝐴𝑄 = (−4).
4
−5
⃗⃗⃗⃗⃗
Express 𝐵𝑄 in component form.
3.
A, B and C have coordinates (2, -3, 5), (7,2,10) and (17, 12, 20), respectively.
Show that A, B and C are collinear and write down the ratio in which B divides AC.
4.
A and B are the points (-3 ,-5,2) and (4,9,9) respectively. T divides AB in the ratio 3:4.
Find the coordinates of T.
5.
P, Q and R have coordinates (1,2,3), (4,-5,6) and (7,-8,9) respectively.
a) Find the coordinates of the point S such that PQRS is a parallelogram.
b) Find the size of angle PQR.
Q
R
Section 3: Straight Lines
6.
A is the point (7,0), B is the point (-3,-2) and C is the point (-1,8).
Draw a sketch of the triangle ABC.
(a)
(b)
(c)
7.
Find the equation of the median through C.
Find the equation of the altitude through B.
Find the coordinates of the point of intersection of the above median and altitude.
OPQR is a kite.
Q is the point (5,2).
Find the gradient of OR, to two decimal places.
y
R
Q
O
8.
P
Three straight lines have equations given by x  y  7 , 3x  2 y  6 and 5x  2 y  23 .
Determine whether the lies are concurrent.
Section 4: Revision
9.
x
Factorise the following
a) x² - x – 6
b) x² - 9x + 14
e) 21x² - 10x + 1
f) 3x² + 4x – 7
10. Find the exact value of x in the
triangles (do not use a calculator)
c) 6a - a²
g) 2z² - 13z + 15
d) 2x² - 3x + 1
h) 6a² + 11a – 10