Question 1: The equation of a line can be determined using two points on the line.
a) Find the vector, parametric, and symmetric equations of the line through the points (-2, 3, 1) and (1, 4, -2).
b) Explain the features of the equations of a line that is parallel to the xz plane, but does not lie on the plane, and is not parallel to any of the axes.
Question 2: Two given lines are either parallel, skew, or intersecting.
a) Determine, if there is one, the point of intersection of the lines given by the equations
(x-1)/(-3)=(y-8)/6=(z-3)/(-2) and (x-8)/4=(y+3)/(-5)=(z-7)/2
b) Given the equations of two lines that meet at the point (-1, 5, 2) and which meet at right angles, but do not use that point in either of the equations. Explain your reasoning.
Question 3: The equation of a plane can be determined using three points on the plane.
a) Find the vector, parametric, and general equations of the plane through the points (2, -3, 1), (3, 1, 6), and (5, -1, 2).
b) Given the equation of a plane that crosses the axes at points equidistant from the origin. Explain your reasoning.
Question 4: A line can either lie on a plane, lie parallel to it or intersect it.
a) Determine, if there is one, the point of intersection between the line given by the equation (x-7)/2=(y-9)/4=(z-4)/3 and the plane given by the equation
b) Determine the angle between the line and the plane.
c) Give the equation of a plane and three lines, one of which is parallel to the plane, one which lies on the plane, and one of which intersects the plane. Explain your reasoning.
Recently Asked Questions
- Returns for the Alcoff Company over the last 3 years are shown below. What's the standard deviation of the firm's returns? (Hint: This is a sample, not a
- Please refer to the attachment to answer this question. This question was created from Chap016.
- Please refer to the attachment to answer this question. This question was created from CHEM+1212K+201602+Recitation+Week+06.docx.