Home 2017 TJC MYE Q4 $ABCD$ is a piece of cardboard in the shape of a trapezium with $angle COA=angle BAO={{90}^{circ }}$, $OA=5$cm, $OC=frac{5sqrt{2}}{3}$cm and $AB=5sqrt{2}$ cm. As part of
Home 2022 SAJC J2 MYE Q5 (a) Relative to the origin $O$, the fixed points $A$ and $B$ are such that $overrightarrow{OA}=mathbf{a}$ and $overrightarrow{OB}=mathbf{b}$. The point $R$ has position vector
Home 2022 RI J1 CT Q8 The earth can be modelled as a sphere, centered at the origin $O$ with radius $r$.A point on the sphere with longitude $varphi $
Home 2022 ACJC J2 MYE Q5 The diagram shows a prism with triangular ends $ABF$ and $DCE$. $AD$, $BC$ and $FE$ are parallel edges of the prism. The rectangular plane
Home 2022 DHS J2 MYE P1 Q10 The plane ${{pi }_{1}}$ contains the point $Aleft( 2,1,-1 right)$ and the line $l$ with equation $frac{x-5}{2}=y$, $z=1$. Another plane ${{pi }_{2}}$ meets
Home 2022 JPJC J2 MYE P1 Q8 The plane ${{p}_{1}}$ has equation $2x-y+3z=0$ and the line $l$ has equation $x=frac{y-1}{a}=frac{z-3}{b}$, where $a$ and $b$ are non-zero constants. The points $A$
2019 MI P1 Q8 (a) Referred to the origin $O$, the point $Q$ has position vector $mathbf{q}$ such that $mathbf{q}=2mathbf{i}-frac{3}{2}mathbf{j}-frac{1}{2}mathbf{k}$. (i) Find the acute angle between $mathbf{q}$ and the $y$-axis.
2022 NYJC J2 CT2 P1 Q6 With reference to the origin $O$, the non-collinear points $A$,$B$ and $C$ are such that $overrightarrow{OA}=mathbf{a}$, $overrightarrow{OB}=mathbf{b}$ and $overrightarrow{OC}=mathbf{c}$. The $M$ is the midpoint
2022 ACJC J2 MYE Q4 (a) Vectors $mathbf{u}$, $mathbf{v}$ and $mathbf{w}$ are such that $mathbf{w}ne mathbf{0}$ and $4mathbf{w}times mathbf{v}=3mathbf{u}times mathbf{w}$. (i) Show that $mathbf{w}=lambda left( 3mathbf{u}+4mathbf{v} right)$, where $lambda $
Home 2022 HCI J2 BT Q2 Relative to the origin $O$, two points $A$ and $B$ have position vectors $mathbf{a}$ and $mathbf{b}$ respectively.It is given that $mathbf{c}$ and $mathbf{d}$ are