Find the position vector of ##Q##

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In summary, to find the position vector of point Q, you need to identify the coordinates of Q in the chosen coordinate system and express it as a vector originating from the origin. Typically, this is represented as Q = (x, y, z) in three-dimensional space, where x, y, and z are the respective coordinates of point Q.
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chwala
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Homework Statement
see attached (highlighted in Red)
Relevant Equations
vectors
O level question; i used similarity would appreciate an easier approach for 2 marks.

1712998784103.png


1712998811995.png



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The ms solution (approach) is not clear to me. Here it is;



1712998905932.png


My approach; using similarity

1712999389794.png


Any insight welcome its a 2 mark question- cannot seem to find easier way though i suspect reflection.
 
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210413PNG.png
 
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  • #3
anuttarasammyak said:
View attachment 343313
...still not getting it. You mind giving some reason or thought. Thks.
 
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Triangle OPC and QPB are similar with ratio 3.
 
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anuttarasammyak said:
Triangle OPC and QPB are similar with ratio 3.
And ΔQOA is similar to each of those two.
 
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FAQ: Find the position vector of ##Q##

What is a position vector?

A position vector is a vector that represents the position of a point in space relative to a reference point, usually the origin of a coordinate system. It is typically expressed in terms of its coordinates in that system, such as (x, y, z) in three-dimensional space.

How do I find the position vector of point Q given its coordinates?

To find the position vector of point Q, simply take its coordinates (x, y, z) and express them as a vector. The position vector can be written as Q = xi + yj + zk, where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

What if point Q is defined in a different coordinate system?

If point Q is defined in a different coordinate system, you will need to convert its coordinates to the desired system. This may involve applying transformations such as translations or rotations, depending on the relationship between the coordinate systems.

Can the position vector of Q be negative?

Yes, the components of a position vector can be negative. A negative component indicates that the point is located in the opposite direction from the origin along that axis. For example, if Q has coordinates (-3, 2, -1), its position vector would be -3i + 2j - k.

How do I find the position vector of Q if I have its distance from the origin?

If you know the distance from the origin to point Q (let's say d) and the direction of the vector (given by a unit vector u), you can find the position vector by multiplying the distance by the unit vector: Q = d * u. Ensure that u is a unit vector (its magnitude is 1) before performing the multiplication.

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