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: Find eguation of a Plane that an contains the vector: and and Z=3E

A:

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

A: .

Q: Let A and B be the points defined by the position vectors a = 3i+j and b = 4i-2j, respectively.…

A: A and B be the points defined by the position vectots,To find,the shortest distance from A to the…

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

A:

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

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: Given points A(8, – 5, 4) and B(-2, 3, 2), find: (a) the distance from A to B; (b) a unit vector…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…