3. (10 points) Find the angle between the following two lines х 1 y 2 +...

Question

Question

3. (10 points) Find the angle between the following two lines х 1 y 2 + 3 Lj: = -1 -4 1 х Y + 2 Z L2 : 2 -2 -1 and give the

math calculus

Answer 1

Answer #1

Direction vectors e, <-1, -4,1) <2, -2, -1) Cosi ē,oēz Tellel angle (-1,-4,1>.< 2,-2 ۹,۰۰۰ > . (اربا - - Cos 1 +16+1 4 +4+1

Answer 2

Similar Homework Help Questions

x =-y+2 = -z+2 The symmetric equations for 2 lines in 3-D space are given as:...

x =-y+2 = -z+2 The symmetric equations for 2 lines in 3-D space are given as: 1. L,: x-2 = -y+1 = z+1 a) Show that lines L1 and L2 are skew lines. b) Find the distance between these 2 lines x =1-t y=-3+2t passes through the plane x+ y+z-4=0 2. The line Determine the position of the penetration point. a. Find the angle that the line forms with the plane normal vector n. This angle is also known as...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d =...

Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
Given lines L1 : Ty (1-1)+(21) -2 1 and L2: y 4 8+t2 3 (a) Find...

Given lines L1 : Ty (1-1)+(21) -2 1 and L2: y 4 8+t2 3 (a) Find the point of intersection of lines Lị and L2. (b) Determine the cosine of the angle between lines L, and L2 at the point of intersection. © Find an equation in form ax +by+cz = d for the plane containing lines L, and Lu. (d) Find the intersection, if any, of the line Ly and the plane P : 3x – 4y + 72...

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...
Q3 (8 points) Find general equation of the plane containing the following two lines: 2 C...

Q3 (8 points) Find general equation of the plane containing the following two lines: 2 C = 2t - 4 LL: = 2t +1 y = - +3 5 +2 and L2:y 2 2 5t - 1
In problems 7-8, find out whether there exists a plane containing the two given lines. If...

In problems 7-8, find out whether there exists a plane containing the two given lines. If there is such a plane, find its equation. Ll: x=2-t, y=3+2+, z = 4+t L2: =l+, y = 5 – 2s, z = 5+ 8. Lị: x=1+t, y = 2 – t, z = -3+ 2t L2: 2 + 2y +2=4, 2-y + 22 = -3

56. Let Li and L2 be the lines whose parametric equations are L]: x = 41,...

56. Let Li and L2 be the lines whose parametric equations are L]: x = 41, y = 1 -21, z = 2 + 21 L2: x = 1+1, y = 1-1, Z=-1+ 41 (a) Show that Li and L2 intersect at the point (2,0, 3). (b) Find, to the nearest degree, the acute angle between L and L2 at their intersection. c) Find parametric equations for the line that is perpen- dicular to L, and L2 and passes through...
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...
K to browse... Q3 (8 points) Find general equation of the plane containing the following two...

K to browse... Q3 (8 points) Find general equation of the plane containing the following two lines: = 2t - 4 ci : y 2t +1 = -t+3 5t+2 and L2: y z 5 - 1

3. Determine the intersection of the two lines, if any: 2 y+1; z 1. 3 L2:...

3. Determine the intersection of the two lines, if any: 2 y+1; z 1. 3 L2: =5-t. y = t, 2 = 1-+3t, t E R L and evaluate the distance between R(1, 1. -1) and Li 3. Determine the intersection of the two lines, if any: 2 y+1; z 1. 3 L2: =5-t. y = t, 2 = 1-+3t, t E R L and evaluate the distance between R(1, 1. -1) and Li