Vectors

2021 CJC Promo Q4 The points $Aleft( 1,0,-2 right)$, $Bleft( 3,-1,-2 right)$ and $Cleft( -3,7,0 right)$ lie on plane ${{p}_{1}}$. Another plane ${{p}_{2}}$ has equation $3x-y+2z=3$. (i) Find a vector

2020 HCI Promo Q9 With respect to an origin $O$, the points $A$,$B$,$C$ and $D$ have position vectors $mathbf{a}=4mathbf{i}$, $mathbf{b}=2mathbf{k}$, $mathbf{c}=3mathbf{i}-5mathbf{j}$ and $mathbf{d}=3mathbf{i}+11mathbf{j}+left( alpha +2 right)mathbf{k}$ where $alpha $ is

2021 JPJC Promo Q6 (a) Given that $mathbf{u}cdot mathbf{v}=0$, what can be deduced about the vectors $mathbf{u}$ and $mathbf{v}$? [2] (b) Referred to an origin $O$, the position vectors of

2021 ASRJC Promo Q8 Relative to origin $O$, the points $A$ and $B$ have position vectors $mathbf{a}$ and $mathbf{b}$ respectively, where $mathbf{a}$ and $mathbf{b}$ are non-zero vectors. The point $C$

2021 DHS P1 Q9 Points $A$ and $B$ have position vectors $left( begin{matrix}1 \q \2 \end{matrix} right)$ and $left( begin{matrix}-1 \0 \1 \end{matrix} right)$ respectively, where $q$ is a positive

2011 MI C2 MYE P2 Q4 [Modified] The line ${{l}_{1}}$ passes through the points $A$ and $B$ which have position vectors $2mathbf{i}-3mathbf{j}+mathbf{k}$ and $3mathbf{i}-mathbf{j}$ respectively. The line ${{l}_{2}}$ has Cartesian

2020 VJC P1 Q7 With reference to the origin $O$, the points $A$, $B$, $P$, $Q$ and $R$ have position vectors $mathbf{a}$, $mathbf{b}$, $mathbf{a}-2mathbf{b}$, $-2mathbf{a}-3mathbf{b}$ and $2mathbf{a}+mathbf{b}$ respectively, where $mathbf{a}$