The distance between the following two skew lines is Line#1: [x, y, z] = [1, 1, 9] + t[1, –3, 0] Line#2: [x, y, z] = [1,0, –3] + 8[2, 2, 0] a. 12 b. 21 С. 3 d. 15 e. 9

Q: 81. Given r = (-3, 4) and s = a. Find the product ||r|||s||. (9. – 12). b. Find r· s. c. Based on…

A: Given:r=-3,4 and s=9,-12Formula:u=u.u

Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: 1. Given the points P(5, 3, - 4) and Q(7 - 1, - 3), find the following: a. the vector PO b. PQl

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Q: Find the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

Q: 2. C. Given that x = 2i+2j–k and y=5i– 3j +2k. i. |x| and i. X*y ii. the angle, 0, between the two…

A: Dot product

Q: 1. Given two vectors, a = nearest degree. [1, 2, 4] and b = [− 6, 0, 3] determine the angle between…

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Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

Q: Find the lengths of triangle PQR. Is it a right triangle? Is the triangle equilateral, scalene, or…

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Q: I. Find the lengths of vectors u and v. Find the angle between ū and v. 1. u = √ = 123' 2. 2 √ = 234

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Q: 6. Find a plane with the P (3, – 4, 5) and contains the line L:= =*

A: It is given that plane passes through (3,-4,5) and the DR's of a given line is 2,-3,5.

Q: i = [4,24, 46] = r·õ+B so that i = [-4, 1,7] and B is perpendicular to

A: Introduction: The dot product of two vectors lies in the same plane as the two vectors. if two…

Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3, 2, 4), and w=(-6,1,1). V

A: Angle between two vector V and W found using cosine function

Q: Let a(t) = (– 5, 5, – 2)t + (2, 4, 6) and b(u) 3 (- 3,0, - 4)и + ( - 2, — 8, — 5). Find the acute…

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Q: Given the vectors v =i+ 3j – 2k and w = 3i – 4j + k. Find the area of the parallelogram with sides…

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Q: Q1.A. For the figure shown below, at what condition the vectors X and Y are orthogonal B -B 1 1

A: Vectors

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. N, = 2î…

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Q: Given the points A(-1, 2, 0), B(1, 0, 3) and C(1, 0, 2), find AB • AC x BC.

A: