Let the points A = (1, 0, 2), B = (3, 3, 1) and C = (−1, 4, 1) and the vector v = (1, 1, 3) a. Find the line r that passes through A and B and the line s that passes through C and is parallel to the vector v. b. Determine whether r and s are coincident, parallel, concurrent, or reverse. If they are competitors, find the intersection point.

Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: Find the vector v = PQ. P = (4,3, 6) Q = (9,5, 3) V =

A:

Q: given the vector, PQ, whose initial point is P(-2,-5) and whose terminal point is Q(3,4) the…

A:

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

A:

Q: For problems 6 and 7, use the points P(-3, 4,2), Q(-1,6, 2), R(5,3, -1) 6. Find a vector…

A:

Q: Determine whether the lines L₁ and L2 given by the vector equations are parallel, perpendicular, or…

A:

Q: For the three given vectors, either show that they are linearly independent or find a nontrivial…

A:

Q: Determine whether the lines L1 and L2 given by the vector equations are parallel, perpendicular, or…

A:

Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

A:

Q: Consider the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3, -1) Find AB and AD,…

A:

Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: Find the equation of the line that passes through the point ( 8, 8, 2) and parallel to the vector .…

A: The vector equation of the line which is passing through the point (h, k, l) and parallel to the…