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We are going to investigate the vector equations of a line x = a + λb and a plane y = a + λb + μc.
This is vector a.
This is vector b. Select vector b the end point of vector a, right-click and choose Multiply Vector, changing the factor to λ. This is the vector λb.
Use Alt-L to type λ.
Select the point (0, 0, 0) and the vectors a and λb, right-click and choose Add Vectors. This is the vector x = a + λb.
Select vector λb the end point of vector a, right-click and choose Line from Vector. Use the Constant Controller to change the value of λ.
Concentrate on the end point of vector x.
This is vector c. Select vector c the end point of vector λb, right-click and choose Multiply Vector, changing the factor to μ. This is the vector μc.
Use Alt-m to type μ.
Select the point (0, 0, 0) and the vectors a, λb and μc, right-click and choose Add Vectors. This is the vector y = a + λb + μc.
Select vectors λb and μc and the end point of vector a, right-click and choose Plane.
Use the Constant Controller to change the values of λ and μ. Concentrate on the end point of vector y.