How to find shortest distance between a line and y axis

518 Views Asked by At

The equation of line is $r=(3,0,0) + \lambda (3,0,-4)$

And the equation of the y axis is x=0 ,z=0

For y axis $r=(0,k,0) + \lambda (0,1,0)$

I know Formula for calculating the shortest distance is : $|\frac {(a_2-a_1). (b_1×b_2)}{(b_1×b_2)}| $

How do i calculate k so that i can find the shortest distance?

1

There are 1 best solutions below

0
On BEST ANSWER

Let the line be $vec r=\vec a+ \lambda \vec b$, and $y$ axis is $\vec r=0+\mu j$ $$S.D=\left|\frac{(\vec a-0).(\vec b \times \vec j)}{|\vec b \times \vec j|}\right|=\left|\frac{(3\vec i-0).((3\vec i-4\vec k) \times \vec j)}{|(3\vec i-4 \vec k) \times \vec j|}\right|=\frac{12}{5}$$