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13 questions
SA-9709-P3-VE5-Q01 1 mark L1 Foundation Calculator Foot of perpendicular
F F F A A A r = a + λ d \mathbf{r}=\mathbf{a}+\lambda\mathbf{d} r = a + λ d F F F
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-Q02 1 mark L1 Foundation Calculator Distances
The shortest distance from a point A A A
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-001 4 marks L2 Standard Calculator Foot of perpendicular
Find the coordinates of the foot of the perpendicular from A ( 5 , 1 , 0 ) A(5,1,0) A ( 5 , 1 , 0 ) r = ( 1 2 − 1 ) + λ ( 2 1 2 ) \mathbf{r}=\begin{pmatrix}1\\2\\-1\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\2\end{pmatrix} r = 1 2 − 1 + λ 2 1 2
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-002 2 marks L2 Standard Calculator Distances
The foot of the perpendicular from A ( 5 , 1 , 0 ) A(5,1,0) A ( 5 , 1 , 0 ) F ( 3 , 3 , 1 ) F(3,3,1) F ( 3 , 3 , 1 ) A A A
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-006 2 marks L2 Standard Calculator Distances
The foot of the perpendicular from A ( 3 , 3 , 1 ) A(3,3,1) A ( 3 , 3 , 1 ) F ( 2 , 1 , 0 ) F(2,1,0) F ( 2 , 1 , 0 ) A A A
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-009 2 marks L2 Standard Calculator Foot of perpendicular
The point P P P r = ( 1 1 1 ) + λ ( 2 − 1 2 ) \mathbf{r}=\begin{pmatrix}1\\1\\1\end{pmatrix}+\lambda\begin{pmatrix}2\\-1\\2\end{pmatrix} r = 1 1 1 + λ 2 − 1 2 O P OP O P λ \lambda λ
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-G01 3 marks L2 Standard Calculator Foot of perpendicular
The line l l l r = ( 1 2 − 1 ) + λ ( 2 1 2 ) \mathbf{r}=\begin{pmatrix}1\\2\\-1\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\2\end{pmatrix} r = 1 2 − 1 + λ 2 1 2 A A A ( 5 , 1 , 0 ) (5,1,0) ( 5 , 1 , 0 ) P P P l l l λ \lambda λ λ \lambda λ A P → \overrightarrow{AP} A P l l l
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-003 4 marks L3 Exam Calculator Distances
Find the exact shortest distance from the origin to the line r = ( 1 1 1 ) + λ ( 2 − 1 2 ) \mathbf{r}=\begin{pmatrix}1\\1\\1\end{pmatrix}+\lambda\begin{pmatrix}2\\-1\\2\end{pmatrix} r = 1 1 1 + λ 2 − 1 2
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-004 3 marks L3 Exam Calculator Foot of perpendicular
The foot of the perpendicular from A ( 5 , 1 , 0 ) A(5,1,0) A ( 5 , 1 , 0 ) l l l F ( 3 , 3 , 1 ) F(3,3,1) F ( 3 , 3 , 1 ) A A A l l l
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-005 4 marks L3 Exam Calculator Foot of perpendicular
Find the coordinates of the foot of the perpendicular from A ( 3 , 3 , 1 ) A(3,3,1) A ( 3 , 3 , 1 ) r = ( 0 1 2 ) + λ ( 1 0 − 1 ) \mathbf{r}=\begin{pmatrix}0\\1\\2\end{pmatrix}+\lambda\begin{pmatrix}1\\0\\-1\end{pmatrix} r = 0 1 2 + λ 1 0 − 1
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-007 3 marks L3 Exam Calculator Distances
B ( 1 , 2 , − 1 ) B(1,2,-1) B ( 1 , 2 , − 1 ) r = ( 1 2 − 1 ) + λ ( 2 1 2 ) \mathbf{r}=\begin{pmatrix}1\\2\\-1\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\2\end{pmatrix} r = 1 2 − 1 + λ 2 1 2 A A A ( 5 , 1 , 0 ) (5,1,0) ( 5 , 1 , 0 ) B A → \overrightarrow{BA} B A B A → ⋅ d ∣ d ∣ \dfrac{\overrightarrow{BA}\cdot\mathbf{d}}{|\mathbf{d}|} ∣ d ∣ B A ⋅ d
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-010 3 marks L3 Exam Calculator Distances
B B B C C C l : r = ( 1 2 − 1 ) + λ ( 2 1 2 ) l:\ \mathbf{r}=\begin{pmatrix}1\\2\\-1\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\2\end{pmatrix} l : r = 1 2 − 1 + λ 2 1 2 λ = 0 \lambda=0 λ = 0 λ = 3 \lambda=3 λ = 3 A ( 5 , 1 , 0 ) A(5,1,0) A ( 5 , 1 , 0 ) l l l 3 3 3 A B C ABC A B C
Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-VE5-008 5 marks L4 Challenging Calculator Distances
The perpendicular distance from A ( 5 , 1 , 0 ) A(5,1,0) A ( 5 , 1 , 0 ) l : r = ( 1 2 − 1 ) + λ ( 2 1 2 ) l:\ \mathbf{r}=\begin{pmatrix}1\\2\\-1\end{pmatrix}+\lambda\begin{pmatrix}2\\1\\2\end{pmatrix} l : r = 1 2 − 1 + λ 2 1 2 3 3 3 λ = 1 \lambda=1 λ = 1 P P P l l l A P = 5 AP=5 A P = 5 λ 1 > λ 2 \lambda_1>\lambda_2 λ 1 > λ 2 λ 1 \lambda_1 λ 1 λ 2 \lambda_2 λ 2
Salam Academy Original Practice · Proposed mark scheme