Determine the direction vector of the following lines where lz is in 3D a) l1:2x – 3y + 6 = 0 %3D - ソー2 4-z b) l2 :3 – x = = c) l3:7 = (1,0) + t(-5,3),t e R 4 -5

Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

A: Given query is to find the value of k.n

Q: 5. Determine a vector equation of the line that passes through the origin and is parallel to the…

A: Determine a vector equation of the line that passes through the origin and is parallel to the line…

Q: Find the vector equation of the line that contains the points (-17, 10,2). r(t)= ( ) +t ( and

A: Answer :

Q: Write a vector equation for the line segment from (-3, 0, 0) to (0, 4, 3).

A: To write a vector equation for the line segment from -3, 0, 0 to 0, 4, 3. To write a vector equation…

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: By finding the extreme values of f, find the shortest distance between Lị and L2. Be sure to fully…

A: Given that L1: v=2,4,4+t4,1,5L2: v=1,−3,2+t−2,3,1 To find the shortest distance between L1 and L2.

Q: Give the vector equation of the line passing through P and Q. P= (3, 1), Q = (2, 0) X = + t

A:

Q: Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the…

A:

Q: A line contains the points P=(−6,−2,−3)P=(-6,-2,-3) and Q=(−4,−3,−6)Q=(-4,-3,-6). A vector equation…

A: