Distance Between Points

To solve this, first find the intersection of the two lines. Parametrize both lines. For the first line, let:

%5Cfrac%7Bx%20-%201%7D%7B2%7D%20%3D%20%5Cfrac%7By%20-%202%7D%7B3%7D%20%3D%20%5Cfrac%7Bz%20-%203%7D%7B4%7D%20%3D%20t.

Thus,

x%20%3D%202t%20%2B%201%2C%20%5Cquad%20y%20%3D%203t%20%2B%202%2C%20%5Cquad%20z%20%3D%204t%20%2B%203.

For the second line, let:

%5Cfrac%7Bx%20-%204%7D%7B5%7D%20%3D%20%5Cfrac%7By%20-%201%7D%7B2%7D%20%3D%20z%20%3D%20s.

Thus,

x%20%3D%205s%20%2B%204%2C%20%5Cquad%20y%20%3D%202s%20%2B%201%2C%20%5Cquad%20z%20%3D%20s.

Equating the expressions for

x

y

, and

z

from both lines, we solve for

s

and

t

. Once the intersection point is found, calculate the distance from

(-1%2C%20-5%2C%20-10)

to the intersection point using the distance formula:

d%20%3D%20%5Csqrt%7B(x_2%20-%20x_1)%5E2%20%2B%20(y_2%20-%20y_1)%5E2%20%2B%20(z_2%20-%20z_1)%5E2%7D.

Chapter Questions
1 MCQs