1) Are the points A(1, 1, 1), B(1, 2, 3), C(-1, 0, 1), and D(2, 2, 2) coplanar?
ID: 2839880 • Letter: 1
Question
1) Are the points A(1, 1, 1), B(1, 2, 3), C(-1, 0, 1), and D(2, 2, 2) coplanar? If not, find the volume of the parallelepiped which has edges AB, AC, AD. (And a few others of course - do you know how many edges does a parallelepiped has?)
2) What is the volume of the largest box in the 1st octant of R^3 with one vertex at the origin and the opposite vertex on the plane 3x + 4y + 5z = 12?
3) What is the cosine of the angle where the curves (t, 2t^2 - 1, t + 1) and (t^2 , t + 2, 2t+ 4) meet?
5) Let L1 be the line through the points (4, -7, 5) and (-1, 3, 0), and L2 be the line through the points (-1, 1, 8) and (4, -4, -7). Write the equations of these lines in both parametric and symmetric form, show that these lines intersect at a right angle, and find the point of intersection.
Explanation / Answer
what is the value of "?" in C(?1,0,1) or is it C(1,0,1)...
if it is C(1,0,1)..then they are not coplanar and parallelopipes has 6 edges AB AC AD and (assuming other corner as E oppossite to A) EB,EC,ED
and increase credit points to get all answers
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