With respect to the origin $$$O$$$, the position vectors of the points $$$A$$$ and $$$B$$$ are given by $$$\overrightarrow{O A}=\left(\begin{array}{r}1 \\ 2 \\ -1\end{array}\right)$$$ and $\overrightarrow{O B}=\left(\begin{array}{r}0 \\ 3 \\ 1\end{array}\right)$ Find the possible position vectors of the point $$$P$$$ on $$$l$$$ such that $$$O P=\sqrt{14}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_32 Year：2021 Question No：10(c)

Answer:

State $\overrightarrow{O P}$ in component form
Form an equation in $\lambda$ by equating the modulus of $O P$ to $\sqrt{14}$, or equivalent
Simplify and obtain $3 \lambda^{2}-\lambda-4=0$, or equivalent
Solve a 3-term quadratic and find a position vector
Obtain answers $2 \mathbf{i}+\mathbf{j}-3 \mathbf{k}$ and $-\frac{1}{3} \mathbf{i}+\frac{10}{3} \mathbf{j}+\frac{5}{3} \mathbf{k}$, or equivalent

Knowledge points:

3.7.3 calculate the magnitude of a vector, and use unit vectors, displacement vectors and position vectors (In 2 or 3 dimensions.)

3.7.4 understand the significance of all the symbols used when the equation of a straight line is expressed in the form r = a +tb, and find the equation of a line, given sufficient information

Answer:

Knowledge points:

Solution:

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