1. ## finding z value

can somebody please help in finding the formula for calculating value of z3 when we have following

a=(x1,y1,z1)

c=(x3,y3,z3)

b=(x2,y2,z2)

c is the point betweent a and b.

2. Originally Posted by charu
can somebody please help in finding the formula for calculating value of z3 when we have following

a=(x1,y1,z1)

c=(x3,y3,z3)

b=(x2,y2,z2)

c is the point betweent a and b.
Dear charu,

Are these three points lie in a straight line???

3. yes, these three points lie in straight line.

4. Originally Posted by charu
yes, these three points lie in straight line.
Dear charu,

Since these three points are in a straight line and given the condition that point "c" lies inbetween points "a" and "b", we could write, (please refer to the attached drawing.)

$\displaystyle z_{3}=\frac{\alpha{z_1}+\beta{z_2}}{\alpha+\beta}$ ; Here the line is divided by "c" to the propotion $\displaystyle \frac{\alpha}{\beta}$

Let $\displaystyle c=\left(x_1+t(x_2-x_1),y_1+t(y_2-y_1),z_1+t(z_2-z_1)\right)$. For any, $\displaystyle 0<t<1$, c will be between $\displaystyle a~\&~b$.