12.5 EXERCISES 1. Determine whether each statement is true or false in R3 (a) Tw

Question

12.5 EXERCISES 1. Determine whether each statement is true or false in R3 (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are parallel (e) Two lines parallel to a plane are parallel. 18. E (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. 19-2 (h) Two planes perpendicular to a line are parallel. inter Two planes either intersect or are parallel. j) Two lines either intersect or are parallel 19. (k) A plane and a line either intersect or are parallel. 2-5 Find a vector equation and parametric equations for the line. l) H20. 2. The line through the point (6, -5, 2) and parallel to the

Explanation / Answer

(a) True.

(b ) False. The x- and y-axes are both perpendicular to the z-axis, yet the x- and y-axes are not parallel.

(c) True.

(d) False. The xy -and yz-planes are not parallel, yet they are both perpendicular to the xz-plane.

(e ) False. The x and y-axes are not parallel, yet they are both parallel to the plane z= 1.

(f) True.

(g) False. The planes y= 1 and z= 1 are not parallel, yet they are both parallel to the x-axis.

(h )True.

(i) True.

(j) False. They can be skew.

(k) True

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.