1. Find the Parametric and Symmetric equations of the line passing through the points (1,5,3) and (2,-4,1).
Answer:
First, we need to find a vector produced by the two
points:
Next, we take the vector and the point (1,5,3) and plug it into the formula
for parametric
equations:
For the symmetric equations, we solve for
in each equation and set all of the equations equal to each
other:
2. Find the linear equation of a plane formed by the vectors <1,1,1> and <3,1,2> at the point (5,-3,2).
Answer:
First we must find the normal vector by taking the cross product of the two
vectors
Then we find the equation by using the
formula:
