Vectors

2019 TMJC Promo Q10 The diagram shows a structure with a horizontal square base $OABC$ and a horizontal square top $DEFG$, where $OA=2$m and $DE=6$m. The vertical height of the

2013 CJC P2 Q2 The line $l$ passes through the point $A$, whose position vector is $-mathbf{i}+mathbf{j}$, and is parallel to the vector $4mathbf{i}-3mathbf{j}+mathbf{k}$ and the plane $p$ has equation

2021 TJC P1 Q11 Coordinates axes $Oxyz$ are set up with the origin $O$ at the base of an airport control tower. The $x$-axis is due East, the $y$-axis due

2021 HCI J2 BT Q7 [Modified] For a school camp, Tom and Jerry stay in a tent which can be modelled by using sheets of cardboard. Cardboard $OABC$ is rectangular

2022 RI P2 Q3 The line ${{L}_{1}}$ has equation $1-y=frac{z-1}{2}$, $x=2$, and meets the $xy$-plane at point $P$. The point $A$ has position vector $left( begin{matrix}3 \-1 \2 \end{matrix} right)$

2022 TMJC P1 Q8 The plane ${{p}_{1}}$ has cartesian equation $x+z=3$. The plane ${{p}_{2}}$ is perpendicular to ${{p}_{1}}$ and contains the line ${{l}_{1}}$ with equation $frac{x+2}{5}=frac{y+1}{2}=frac{3-z}{3}$. (i) Show that the

Home 2023 HCI J2 MYE P2 Q3 (a) Given that $mathbf{u}$, $mathbf{v}$ and $mathbf{w}$ are nonzero vectors such that $mathbf{u}=mathbf{v}times mathbf{w}$, state the geometric relationship that $mathbf{u}$ has with $mathbf{v}$

Home 2013 RVHS P1 Q9 Referred to an origin, $O$, the position vectors of two points $A$ and $B$ are $mathbf{a}$ and $mathbf{b}$ respectively. $mathbf{a}$ and $mathbf{b}$ are not parallel.