math- calculus question
Write down a vector equation for the line, L1, that passes through the point P = (-7,2, 4) and is orthogonal to both a ->= (0, -9, 1) and b->= 3i->+j-> -4k->..
(b) Construct another line, L2, so that L1and L2 are skew. Be sure to demonstrate that they are skew.
Homework Answers
Let L1 be the line passing through thr points Q1=(-4,-5,-2) and Q2=(0,-7,2). Find a value of...
Let L1 be the line passing through thr points Q1=(-4,-5,-2)
and Q2=(0,-7,2). Find a value of k so the line L2 passing through
the point P1=(7,-9,k) with direction vector d=[-1,-1,0]^t
intersects with L1
K=??
Question 2 [10 points) Let Ly be the line passing through the points Or.-5. 2) and Q-0-72) Find a value of k so the line passing through the point Ps-P;(7.-9. k) with direction vector i/-/-1,-1.0" intersects with L ko
(1) (a) Find the equation of the line, Li, which passes through the points A :...
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i =...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u...
please answer question 4-7
Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
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...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
I cannot get i) or j) 3. (20 marks) Consider the parallel lines L, : x=...
I cannot get i) or j)
3. (20 marks) Consider the parallel lines L, : x= -3 +8 2 [1] and L2: x = 0 + [2] 4. and 11 [3 -21 the planes P1 : 3x + 2y + 2z = -7 and P2 : 2.x – 2y - 2 = 11. (a) Find the equation of a plane in standard form containing both L, and L. (b) Find an equation of the line of intersection of P, and...
Vector equation of line - Pyramid
(a) Write down the equation of the line l through the centre of the squarebase that is perpendicular to the base.(b) Use the fact that the vertex D is on the line l together with the factthat the length of the sloping side is a to calculate the position vector ofthe point D with respect to the origin O in terms of a and the unitvectors i, j and k.(c) Hence write down the equation of the line that passes...
3. Consider the two planes, P and P2, where Pi is given by the general equation 2x y+2-5 and P2 passes through the points (0,0,-1), (3,2,4) and (2, 4,5). (a) Find L, the line of intersection of the t...
3. Consider the two planes, P and P2, where Pi is given by the general equation 2x y+2-5 and P2 passes through the points (0,0,-1), (3,2,4) and (2, 4,5). (a) Find L, the line of intersection of the two planes. (b) Suppose another line, L2, has vector equation (x, y, z) = (8,3,-2) + t2(-2, 1, 1). 6 marks] Find where Land L2 intersect 4 marks
3. Consider the two planes, P and P2, where Pi is given by the...
Let L1 be the line passing through the point P 2, 2,-1) with direction vector a=[-1,...
Let L1 be the line passing through the point P 2, 2,-1) with direction vector a=[-1, 1,-2]T, and let L2 be the line passing through the point P2-(-5, -5,-3) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that dQ1Q2) d. Use the square root symbol' where needed to give an exact value for your answer. d 0 Q1-(0, 0, 0)...
Let L1 be the line passing through thr points Q1=(-4,-5,-2)
and Q2=(0,-7,2). Find a value of k so the line L2 passing through
the point P1=(7,-9,k) with direction vector d=[-1,-1,0]^t
intersects with L1
K=??
Question 2 [10 points) Let Ly be the line passing through the points Or.-5. 2) and Q-0-72) Find a value of k so the line passing through the point Ps-P;(7.-9. k) with direction vector i/-/-1,-1.0" intersects with L ko
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
please answer question 4-7
Prove the arithmetic properties of the Cross Product 1. 2. a. Line L1 is parallel to the vector u Si+j, line L2 is parallel to the vector u-3i +4j and both lines pass through point P(-1,-2). Determine the parametric equations for line L1 and Lz b. Given line L:x(t)-2t+8,y(t)-10-3t. Does L and Ls has common 3. a. Find the equation of the plane A that pass through point P(3,-2,0) with b. Given A2 be the plane...
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...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
I cannot get i) or j)
3. (20 marks) Consider the parallel lines L, : x= -3 +8 2 [1] and L2: x = 0 + [2] 4. and 11 [3 -21 the planes P1 : 3x + 2y + 2z = -7 and P2 : 2.x – 2y - 2 = 11. (a) Find the equation of a plane in standard form containing both L, and L. (b) Find an equation of the line of intersection of P, and...
3. Consider the two planes, P and P2, where Pi is given by the general equation 2x y+2-5 and P2 passes through the points (0,0,-1), (3,2,4) and (2, 4,5). (a) Find L, the line of intersection of the two planes. (b) Suppose another line, L2, has vector equation (x, y, z) = (8,3,-2) + t2(-2, 1, 1). 6 marks] Find where Land L2 intersect 4 marks
3. Consider the two planes, P and P2, where Pi is given by the...
Let L1 be the line passing through the point P 2, 2,-1) with direction vector a=[-1, 1,-2]T, and let L2 be the line passing through the point P2-(-5, -5,-3) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that dQ1Q2) d. Use the square root symbol' where needed to give an exact value for your answer. d 0 Q1-(0, 0, 0)...
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