Find the coordinates of the point where the line through (5, 1, 6) and (3, 4,1) crosses the YZ – plane.

Solution:

It is known to us that the vector eq. of a line passing through two points with position vectors and is given as

Therefore the position vector of point is given as

And the position vector of point is given as

Therefore subtract eq.(2) and eq.(1) we obtain

Let the coordinates of the point where the line crosses the YZ plane be So,

As the point lies in line, it satisfies its eq.,

Substituting eq.(4) in eq.(3) we obtain,

It is known to us that, two vectors are equal if their corresponding components are equal

Therefore,
And,

Substituting the value of in eq. and , we obtain

And

As a result, the coordinates of the required point is .