Solution 1: The system of linear equations.

Solution 1: The system of linear equations
Given that
So, the required system of equation is:
a): The augmented matrix is
b): Let’s perform row operations to find row echelon form of matrix.
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c): From part (b), the general solution is
,
d): The above solution is the intersection of three planes in four dimensions that does not
passes through the origin.
Solution 2: Given plane and line
We know that the angle between a line and a plane is equal to the complementary acute
angle that forms between the direction vector of the line and the normal vector of the
plane. If the direction vector and normal vector then
Here, and
So,

Solution 3: Given plane with equation . The normal
vector to the plane is
, and point
So, the equation line that passes through the point and in the direction of
is
Solution 4: Given parametric equation is and equation
of plane is . Since, parametric equation intersects the plane. This implies
that the parametric equation satisfied the plane.
So,