1. Given a line P(t) through the points Po = [1,0|7 and P [2,4]7 in 2D (a) Extend P(t) to homogeneous coordinates (b) Compute the intersection of P(t) with the homogeneous plane 2 3h in homogeneous cOordinates (c) What is the point of intersection in non-homogeneons coordinates ?

Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

A:

Q: 2. a) Determine the equation of the line ℓ passing through the points (2, 1, 3) and (3, 2, 6). b)…

A: Step 1: Step 2: Step 3: Step 4:

Q: ii. Use the basic definition of complex integration to evaluate the integral I $, z¹ dz, where the…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the value of k so that the line [x, y, z] = [2, -2, 0] + t[3, 5, k] is parallel to the plane 4x…

A:

Q: Let A = (2, 1, 1), B = (2, 3, 1), and C = (4, 5, 1). a) An equation for the plane that contains A…

A:

Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

A:

Q: 3. Find an equation for the plane in R³ containing the points P = (4, 1, 0) Q=(3, 2, 1) R = (5, 1,…

A: The given points are, P=(4,1,0)Q=(3,2,1)R=(5,1,1). Let an equation containing three points…

Q: 1) Consider the two planes x 2y + z = -5 and 3x 2y - z = 1 (a) Find an equation for the line of…

A: The solution is given as follows

Q: What is the projection of r(t) = ti + t4j + etk onto the xz-plane?

A: Given: r(t)= ti+t4j+etk

Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

A: