Given points A(8, – 5, 4) and B(-2, 3, 2), find: (a) the distance from A to B; (b) a unit vector directed from A towards B; (c) a unit vector directed from the origin toward the midpoint of the line AB; (d) the coordinates of the point on the line connecting A to B at which the line intersects the plane z = 3.

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

Q: Let P and Q be the points in R3 with position vectors p = (4, -6, 1) and q = (1, -3, -5),…

A:

Q: 1. Give the vector equation of a line perpendicular to the line L: x= 21-1, y=-31, 1 e R. Are there…

A: Given line: l:x=2t-1, y=-3t, t∈ℝ To find the other line The vector equation of the line is…

Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

A:

Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: a) Find Ivl if v = -7i - 6j. Give exact value. b) Graph the vector v in the coordinate plane.

A: Solve the following

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: