Q9) The diagram ( in the attatchment) shows a point P with co-ords (4,2,6) & two points S & T which lie on the x-axis. If P is 7 units from S & 7 units from T, find the co-ords of S & T.
I was wondering if you could somehow split the diagram in2 2 separate right-angled triangles (I've done that in red in2 the diagram, but i aint sure...Then you could use the vectors of the right angle triange & use the scalar product set = 0 since the angle = 90 degrees. Lol, Plz help..I'm so confuzzled. =)
Not totally sure if this is correct makes or sense but:
First find shortest distance, d from P to x-axis using Pythagoras
d2= 62 + 22
(This is the distance from P to the point on the x-axis with the x coordinate of P i.e. (4,0,0), this having to be the shortest distance)
Like you said you can now construct two right angle triangles from the isoceles triangle PST, with the mid point of ST being the point on the x axis closest to P.
/| 7 / | root 40 /__| a
Therefore S and T are +/- 3 from the point on the x-axis closest to P, (4,0,0) and therefore have coordinates S(1,0,0) or T(7,0,0)
Hey, umm...is that what u did with the pythagoras part?? (in attatchment)