(1 point) The planes 3x + 4y + z = 2 and 3x – 3y =...

Question

Question

(1 point) The planes 3x + 4y + z = 2 and 3x – 3y = -18 are not parallel, so they must intersect along a line that is common t

math algebra

Answer 1

Answer #1

Given that the planes 3x+4y+z=2 and 3x-3y=-18 are not parallel , so they must intersect along a line that is common to both of them .

For finding the intersecting line now we solve the equations ,

3x+4y+z=2 and 3x-3y=-18

These are two equations of three variables so we have a free variable .Let z = t then we get ,

3x+4y=2-t and 3x-3y=-18

Solving these equations we get , 7y=20 - t and 7x= -22 - t

That means , y = (20 - t)/7 and x = (-22 - t)/7

Therefore (x,y,z)=((-22 - t)/7 , (20 - t)/7, t )

=(-22/7 , 20/7 , 0) + t*(-1/7 , -1/7 ,1)

Thus the vector parametric equation for the intersecting line is

L(t) = (-22/7 , 20/7 , 0) + t*(-1/7 , -1/7 , 1)

Answer 2

Similar Homework Help Questions

Question 12 Find parametric equations for the line of intersection of the planes - 2y+z= 1...

Question 12 Find parametric equations for the line of intersection of the planes - 2y+z= 1 and 2x + y - 3x = -3. Does the line L intersect the plane 2x - y - 3x = 1? If so, at what point? Note: This is the review exercise at the end of Lecture 2.
(1 point) Give a geometric description of the following system of equations 1 2x + 4y...

(1 point) Give a geometric description of the following system of equations 1 2x + 4y - 6z Two parallel planes = " -3- 6y + 9x = 2x + 4y - 62 = Two parallel planes 2. ** –3x - 6y + 9z = 4y - O2 = Two planes intersecting in a line 73. 21 * -x + 5y - 92 = 12 16 –12 18 12 1 T
Please help with these problems. 8. Consider the two planes listed below 2x - y +...

Please help with these problems. 8. Consider the two planes listed below 2x - y + z = 1 +y-2=2 These two planes intersect at a right angle. Show that this is true by showing their normal vectors are perpendicular. Find the parametric equations of their line of intersection. Is the line of intersection (call this L) for these planes parallel, perpendicular (intersect at 90 degrees), skew (not parallel, don't intersect), or none of the above to the line: F(t)...

Please provide clear handwritings for answers and specific step by step explanations of questions 3 and 4. Thank you. 3. Are the plane 6z 3y - 4z-12 and line L 2, y 32t, z2-2t parallel? If so, find...

Please provide clear handwritings for answers and specific step by step explanations of questions 3 and 4. Thank you. 3. Are the plane 6z 3y - 4z-12 and line L 2, y 32t, z2-2t parallel? If so, find the distance between them. If they are not parallel, but are intersecting (at a single point), find the point of intersection. If they are none of the above, draw a cat. 4. The line r(t) = 〈1, 1,1〉 +t(1,3,-1) and the plane...
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x +...

2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x + 4y = -6 x=2, y=-3 | 4, 2y- 6x =7 3x - y=9 No solution/Parallel lines
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y =...

QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...

Consider the following geometrical objects in R3: li: x=2 -21, y = -1, z = 2,...

Consider the following geometrical objects in R3: li: x=2 -21, y = -1, z = 2, ER 12: (x, y, z) = (0,5, -1) + (2, -1, 1), 1ER II : 3x + 4y - 2z = 1 II2 : 3x + 3y + z = -1 (a) Find the intersection point of , and 2. (b) Find the line 63 containing A(2,3,4) and is parallel to both II, and II. (c) () Determine whether II, and 2 are intersecting,...
(1 point) Consider the planes -2x1 + 4x2 + 4x3 =-2 -5x1-52 +5x3 25 a. Find...

(1 point) Consider the planes -2x1 + 4x2 + 4x3 =-2 -5x1-52 +5x3 25 a. Find a point P that is on both planes. P (0, 0,-10) b. Find a vector v that is parallel to both planes. c. Find a vector equation for the intersection of the two planes. x(t)3,-2,0 t <-40, 10, -30
3. (14 points) Given the lines: 21:2(t) = -3t – 1, y(t) = 2t +4, z(t)...

3. (14 points) Given the lines: 21:2(t) = -3t – 1, y(t) = 2t +4, z(t) =t+4 12: x(u) = 5 - 3u, y(u) = u +1, (u) = u +2 1. Determine whether li and ly are parallel, skew or intersect. If the lines intersect, find the point of intersection of li and 12. 2. If the lines intersect or are parallel, give an equation for the plane which contains both lines. If the lines are skew, find a...

the straight line L1 is described by the equation 3x + 4Y + 5 = 0....

the straight line L1 is described by the equation 3x + 4Y + 5 = 0. the straight line L2 is perpendicular to L4. lines L1 and L2 intersect at the point (1, -2) Give an example of another point than (1, -2) located on L2