Edexcel MECHANICS 1 VECTORS
Main ideas Given that 𝒓𝑨 is the position vector of the particle A , and 𝒓𝑩 is the position vector of the
particle B
1) Given 𝒓𝑨 = (1 i – 4j ) and 𝒓𝑩 = ( 5 i ) , Find the bearings of B from A.
2) Given 𝒓𝑨 = ( 3 i + 4 j) and 𝒓𝑩 =( 8 i -1j ), Find the bearings of B from A.
3) Given 𝒓𝑨 =( - 1 i + 5 j) and 𝒓𝑩 = ( - 1 i - 7j ), Find the bearings of B from A.
4) Given 𝒓𝑨 = ( - 1i + 2 j ) and 𝒓𝑩 = ( - 6 i+ - 3j ), Find the bearings of B from A.
5) Given 𝒓𝑨 = ( 6 i + 3j ) and 𝒓𝑩 = ( 1 i + 3 j ) , Find the bearings of B from A.
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Edexcel MECHANICS 1 VECTORS
6) Given 𝒓𝑨 = ( 5 i+ 4j ) , 𝒓𝑩 =(-11i + kj ) and B is on a bearing of 𝟑𝟏𝟓° from A.
Find the value of 𝒌
7) 𝒓𝑨 =( 5 i + 4 j ) and
8) 𝒓𝑨 ( 5 i + 14 j ) and
9) 𝒓𝑨 = ( 5 i + 14j ) and
𝒓𝑩 = (11 i + k j ) given B is due east of A
𝒓𝑩 ( k i + 5 j ) given B is due south of A
𝒓𝑩 ( k i + 5 j ) given B 15 distance units from of A
10) 𝒓𝑨 = ( 2- k)i + (-10 + 6 k ) j and 𝒓𝑩 = ( -26+3k ) i + ( 4+4 k ) j given B and A overlap
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Edexcel MECHANICS 1 VECTORS
EXAMPLES TO APPLY
11) At 𝒕 = 𝟎 , player P and a ball B started to move , 𝒕 seconds later the player and the ball have the
position vectors 𝒑⃗ and 𝒒⃗ respectively ,
where 𝒑⃗ =
𝟐𝐭
−𝟏𝟐 + 𝟒𝒕
𝒎 , and 𝒃⃗ =
m
𝟐𝒕
𝟏𝟐
Given that the player intercepts the ball at point P .Find
a) Show that when 𝒕 = 2 the ball is on a bearing of 𝟏𝟑𝟓° from the player
b) The value of 𝒕 when they meet
c) The position vector ( the location ) of P
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Edexcel MECHANICS 1 VECTORS
12) the position vector of a moving ship S is given by 𝒔⃗ =
𝟑𝒕 + 𝟗
𝒌𝒎
𝟒𝒕 – 𝟔
A lighthouse L is located at the point with position vector (18i + 6j) km.
When t = T, the ship S is 10 km from L.
Find the possible values of T.
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Edexcel MECHANICS 1 VECTORS
13) A particle P is moving and its position is given by 𝒑⃗ =
point with position vector (–4i – 7j) m. Find
𝒌 − 𝟑𝒕
𝒎 + 𝟐𝒕
m . At time t = 6 s, P is at the
a) the value of 𝒌 and the value of 𝒎
b) the distance of P from the origin at time t = 2 s.
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Edexcel MECHANICS 1 VECTORS
14) At time t hours after noon, the position vector of S is 𝒔⃗ km. . 𝒔⃗ =
𝟒𝟎 − 𝟏𝟐𝒕
−𝟔 + 𝟕. 𝟓𝒕
A fixed beacon B is at the point with position vector (7i + 12.5j) km.
a) Find the moment when S is due north of B.
(2)
b) Find the distance of S from B when S is due north of B.
(2)
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Edexcel MECHANICS 1 VECTORS
15) Two ships P and Q are travelling at night with constant velocities.
At midnight, P is at the point with position vector (20i +10j) km relative to a fixed origin O.
At the same time, Q is at the point with position vector (14i –6j) km. .
At time t hours after midnight, the position vectors of P and Q are p km and q km respectively.
Given that 𝒑 = (𝟐𝟎𝒊 + 𝟏𝟎𝒋) + (𝟑𝒊 + 𝟖𝒋)𝒕
And
𝒒 = (𝟏𝟒𝒊 – 𝟔𝒋) + 𝟏𝟐𝒕 𝒋
At time t hours after midnight, the distance between P and Q is 𝒅 km.
(a) By finding an expression for 𝑷𝑸⃗ show that
𝒅𝟐 = 𝟐𝟓𝒕𝟐 – 𝟗𝟐𝒕 + 𝟐𝟗𝟐.
(b) Find the time when the two ships are 18 km apart
(c) Fin the time when the two ships are closest to each other
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Edexcel MECHANICS 1 VECTORS
Remember that
1) the direction of motion is direction of velocity
2) the resultant force is parallel to the acceleration
3) if two particle A and B are due EAST OR WEST of each other
i)
then they have the same y-component
or
ii)
the vector AB connecting them has the y-component zero
4) if two particle A and B are due NORTH OR SOUTH of each other
i)
then they have the same X-component
or
ii)
the vector AB connecting them has the X-component zero
5) If B is due north east of A then AB is parallel to ( i + j )
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