I hope you have a great time.
Please could you show me how to solve the following questions, by steps if possible:
Q1- Find the components of all vectors v which have length 2 and are perpendicular to both the lines
x = 4 + 3t, y = 2 − t, z = 1 + 5t and x − y + z = 2, 3x + 2y − 4z = 6.
Q2- Find the equation of the plane, simplified as much as possible, that contains the point where the
line x = −1 + 2t, y = −4 + 2t, z = 1 − 4t intersects the xz-plane, and is perpendicular to the line
Q3- Prove that if A, B, and C are three points in space, then the area of triangle ABC can be
calculated with the formula
Area of triangle ABC = 1/2|AB × AC|.
I would really appreciate your help