Answer:
Our point is (16/3,17/3,11/3)
Step-by-step explanation:
We will need to find a point in line that goes though P and Q.
To find this line we will need a point in the line (which can be P or Q) and a poiting vector V. This vector can be found subtracting P and Q. V=Q-P
V=(6, 7, 7) - (4, 3, −3)= (2,4,10)
the parametric equation r(t) = P+V*t for the line where will replace out values P and V:
r(t)=(4, 3, −3)+r*(2,4,10) our new point must fulfill this equation for a given t
On the other hand out point A must fulfill that the distance from P is twice its distance from Q.
If we choose a point in between the points and call the distance between P and Q 1, A must be 1/3 of the way to Q and 2/3 of the way to P.
Since the starting point for our parametric equation is P, replacing r for 2/3 on the parametric equation will give us a point r(2/3) that is in the line and is twice as far from P than it is from Q
A=r(2/3)=(4, 3, −3)+2/3*(2,4,10)=(16/3,17/3,11/3)
