Find the unit vector in the direction of .
Given that , find the value of each of the constants and .
Relative to an origin , the points and have position vectors respectively.
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Find the unit vector in the direction of .
Given that , find the value of each of the constants and .
Relative to an origin , the points and have position vectors respectively.
[1]
[1]
[1]
[1]
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The parallelogram is such that and . The point lies on such that = . The point lies on such that =.
Show that , where is an integer to be found.
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In the diagram , , and . The lines and intersect at .
Find in terms of and .
Find in terms of and .
Given that , find in terms of .
Given that , find in terms of .
Find the value of and of .
Find the value of .
Find the value of .
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The diagram shows the triangle . The point is the midpoint of . The point lies on such that intersects at the point where . It is given that and .
Find in terms of and , giving your answer in its simplest form.
Find AC in terms of a and b.
Given that , find in terms of , and .
Given that , find the value of and of .
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The vectors and are such that and .
Find the value of each of the constants and such that .
Hence find the unit vector in the direction of .
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A particle is initially at the point with position vector and moves with a constant speed of in the same direction as .
Find the position vector of after .
As starts moving, a particle starts to move such that its position vector after is given by .
Write down the speed of .
Find the exact distance between and when , giving your answer in its simplest surd form.
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Relative to an origin , the position vectors of the points and are
Find the unit vector in the direction of .
The point is the mid‑point of . Find the value of and of .
The point lies on such that is . Find the value of such that is parallel to the ‑axis.
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In this question all distances are in km.
A ship sails from a point , which has position vector , with a speed of in the direction of
Find the velocity vector of the ship.
Write down the position vector of at a time hours after leaving .
At the same time that ship sails from , a ship sails from a point , which has position vector , with velocity vector .
Write down the position vector of at a time hours after leaving .
Using your answers to parts (b) and (c), find the displacement vector at time hours.
Hence show that .
Find the value of when and are first apart.
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The position vectors of three points, , relative to an origin , are respectively. Given that = , find the unit vector in the direction of .
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The diagram shows a triangle such that and . The point lies on such that . The point is the mid-point of . The lines and are extended to meet at the point . Find, in terms of and ,
Find
Find . Give your answer in its simplest form.
It is given that , where are positive constants.
Find in terms of .
Find in terms of .
Hence find the value of and of .
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