CAIE IGCSE Additional Math 13 Vectors in Two Dimensions Topic Practice

$\mathbf{b}-\mathbf{a}=\frac{p}{p+q}(\mathbf{c}-\mathbf{a})$ oe

AND

Correct completion to given answer
$$\mathbf{b}=\frac{q \mathbf{a}+p \mathbf{c}}{q+p}$$

B4 for $\mathbf{b}-\mathbf{a}=\frac{p}{p+q}(\mathbf{c}-\mathbf{a})$

OR

B1 for $\overrightarrow{A B}=\frac{p}{p+q} \overrightarrow{A C}$ soi

B1 for $\overrightarrow{A B}=\mathbf{b}-\mathbf{a}$ soi

B1 for $\overrightarrow{A C}=\mathbf{c}-\mathbf{a}$ soi

Alternative 1

q(b-a)=p(c-b) oe

AND

Correct completion to given answer
$$\mathbf{b}=\frac{q \mathbf{a}+p \mathbf{c}}{q+p}$$

B4 for q(b-a)=p(c-b)

OR

B1 for $q \overrightarrow{A B}=p \overrightarrow{B C}$ soi

B1 for $\overrightarrow{A B}=\mathbf{b}-\mathbf{a}$ soi

B1 for $\overrightarrow{B C}=\mathbf{c}-\mathbf{b}$ soi

Alternative 2

$\mathbf{b}=\mathbf{a}+\frac{p}{p+q}(\mathbf{c}-\mathbf{a})$ oe

or $\mathbf{b}=\mathbf{c}+\frac{q}{p+q}(\mathbf{a}-\mathbf{c})$ oe

AND

Correct completion to given answer
$$\mathbf{b}=\frac{q \mathbf{a}+p \mathbf{c}}{q+p}$$

B4 for $\mathbf{b}=\mathbf{a}+\frac{p}{p+q}(\mathbf{c}-\mathbf{a})$ oe

or $\mathbf{b}=\mathbf{c}+\frac{q}{p+q}(\mathbf{a}-\mathbf{c})$ oe

OR

B1 for $\overrightarrow{O B}=\overrightarrow{O A}+\overrightarrow{A B}$

or $\overrightarrow{O B}=\overrightarrow{O C}+\overrightarrow{C B}$ soi

B1 for $\overrightarrow{A B}=\frac{p}{p+q} \overrightarrow{A C}$

or $\overrightarrow{C B}=\frac{q}{p+q} \overrightarrow{C A}$ soi

B1 for $\overrightarrow{A C}=\mathbf{c}-\mathbf{a}$ or $\overrightarrow{C A}=\mathbf{a}-\mathbf{c}$ soi