Practise questions · Salam Academy

SA-9709-P3-VE-0012 marksL1 FoundationCalculatorMagnitude

The points

A

and

B

have position vectors

\overrightarrow{OA}=2\mathbf{i}-\mathbf{j}+4\mathbf{k}

and

\overrightarrow{OB}=5\mathbf{i}+3\mathbf{j}+4\mathbf{k}

. Find

|\overrightarrow{AB}|

.

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SA-9709-P3-VE1-0011 markL1 FoundationCalculatorMagnitude

Find

|3\mathbf{i}-4\mathbf{j}+12\mathbf{k}|

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0023 marksL1 FoundationCalculatorPosition vectors

A

is

(2,-1,5)

and

B

is

(6,3,-1)

. Find the coordinates of the midpoint

M

of

AB

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-G013 marksL1 FoundationCalculatorMagnitude

\overrightarrow{OA}=3\mathbf{i}-\mathbf{j}+2\mathbf{k}

and

\overrightarrow{OB}=\mathbf{i}+3\mathbf{j}+2\mathbf{k}

. Find the components of

\overrightarrow{AB}

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-Q011 markL1 FoundationCalculatorPosition vectors

A

and

B

have position vectors

\mathbf{a}

and

\mathbf{b}

. Then

\overrightarrow{AB}

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE-Q011 markL1 FoundationCalculatorMagnitude

\left|\mathbf{i}+2\mathbf{j}+2\mathbf{k}\right|

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE-0023 marksL2 StandardCalculatorMagnitude

Find the unit vector in the direction of

\mathbf{v}=2\mathbf{i}-6\mathbf{j}+3\mathbf{k}

. Give each component as an exact fraction.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0033 marksL2 StandardCalculatorPosition vectors

A

is

(1,4,-2)

and

B

is

(7,1,4)

. The point

P

lies on

AB

with

AP:PB=1:2

. Find the coordinates of

P

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0043 marksL2 StandardCalculatorPosition vectors

ABCD

is a parallelogram (vertices in that order) with

A(1,0,2)

,

B(4,1,3)

and

C(6,5,1)

. Find the coordinates of

D

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0052 marksL2 StandardCalculatorPosition vectors

The points

A(1,2,3)

,

B(3,5,4)

and

C(7,k,6)

are collinear. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0063 marksL2 StandardCalculatorMagnitude

Find the vector of magnitude

15

in the same direction as

2\mathbf{i}-2\mathbf{j}+\mathbf{k}

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0072 marksL2 StandardCalculatorMagnitude

The vector

\mathbf{p}=4\mathbf{i}+k\mathbf{j}+8\mathbf{k}

has magnitude

9

, and

k>0

. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0084 marksL4 ChallengingCalculatorMagnitude

\mathbf{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}

and

\mathbf{b}=2\mathbf{i}-\mathbf{j}+2\mathbf{k}

. Find the two values of

t

for which

|\mathbf{a}+t\mathbf{b}|=\sqrt{26}

.

Salam Academy Original Practice · Proposed mark scheme

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