Equation Of A Line In Space

Concept: The equation of a line passing through points

A

and

B

can be written using vector form:

(x%2Cy%2Cz)%20%3D%20(x_1%2Cy_1%2Cz_1)%20%2B%20t(x_2-x_1%2C%5C%3By_2-y_1%2C%5C%3Bz_2-z_1)

Step 1: Find the parametric form of the line. Points:

A%3D(1%2C1%2C1)%2C%20%5Cquad%20B%3D(2%2C2%2C2)

Direction ratios:

(2-1%2C2-1%2C2-1)%3D(1%2C1%2C1)

Thus,

(x%2Cy%2Cz)%3D(1%2C1%2C1)%2Bt(1%2C1%2C1)

x%3D1%2Bt%2C%5Cquad%20y%3D1%2Bt%2C%5Cquad%20z%3D1%2Bt

Step 2: Substitute into the plane equation.

x%2By%2Bz%3D9

(1%2Bt)%2B(1%2Bt)%2B(1%2Bt)%3D9

3%2B3t%3D9

t%3D2

Step 3: Find the intersection point.

x%3D1%2B2%3D3%2C%5Cquad%20y%3D3%2C%5Cquad%20z%3D3

Thus, the point of intersection is:

(3%2C3%2C3)

Chapter Questions
1 MCQs