Edexcel IGCSE Math B 8.E Vector Sums & Differences Question Bank

Practise expressing diagram paths as sums or differences of given vectors and simplifying the resulting coefficients.

Exam points

construct a required route by adding successive directed vectors
reverse a segment by negating its vector before combining terms
use midpoint or parallelogram relationships to simplify a vector in terms of the given bases

[Maximum number: 2]

Figure 1 shows triangle OAB in which $\overrightarrow{O A}=4 \mathbf{a}$ and $\overrightarrow{O B}=8 \mathbf{b}$
P is the point on OA such that O P: O A=1: 4

(a)

Express in terms of a or bor a and b where appropriate,

[ 2 ]

(i)

$\overrightarrow{A B}$

$\overrightarrow{AB}=8\mathbf{b}-4\mathbf{a}$

B1.

(b)

R is the point on AB such that AR : AB = 1 : n where n is a constant.

Find and simplify an expression for $\overrightarrow{PR}$ in terms of n, a and b.

[ 2 ]

NB: candidates must use vectors as required by the question.

$\overrightarrow{PR}=\overrightarrow{PA}+\overrightarrow{AR}$ $\overrightarrow{PR}=3\mathbf{a}+\frac{1}{n}(8\mathbf{b}-4\mathbf{a})$ $\overrightarrow{PR}=\left(3-\frac{4}{n}\right)\mathbf{a}+\frac{8}{n}\mathbf{b}$

Equivalent form:
$\overrightarrow{PR}=\frac{(3n-4)\mathbf{a}+8\mathbf{b}}{n}$

M1.
A1.

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8.E Vector sums and differences question 1

Question (a)

Question (i)

Question (b)