Let L, be the line in R³ which is given by the vector equation p = s Let L2 be the line in R³ through the points A(1,1,1) and B(1,2,3). Find the pair of points P, and P2 in R³, with P¡ on L1 and P2 on L2 so that these are as close as possible among points on these lines.

Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

A: The equation of the line passing through the point x1, y1, z1 and having direction ratios l, m, n is…

Q: Let u = [-4,0,2], v = [0,6,-4] and w=[-4,6,2]. Find the values x, y, z such that the vector [8, -60,…

A:

Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

A:

Q: Let P(-1, 1, 3) and Q(-3, 1, 5) be points in R3. Find the components, magnitude and direction angles…

A:

Q: Let L7 be the line passing through the points Q1=(3,-5, –1) and Q2=(0, 4, –10). Find a value of k so…

A: Given that L1 be the passing through the points Q1=(3,-5,-1) and Q2=(0,4,-10). And the line  L2 be…

Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

A:

Q: Let / be the line through the point with coordinates (0,0,1) in the direction of the vector…

A:

Q: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

A:

Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

A:

Q: If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K.…

A: A field K is said to be algebraically closed if every polynomial with coefficients in K has a root…

Q: Let L₁ be the line passing through the points Q₁(-4, 5, −5) and Q₂(−1, 6, –2 and let L₂ be the line…

A: This is a question of 3D geometry and vector analysis.

Q: By finding the extreme values of f, find the shortest distance between Lị and L2. Be sure to fully…

A: Given that L1: v=2,4,4+t4,1,5L2: v=1,−3,2+t−2,3,1 To find the shortest distance between L1 and L2.

Q: P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane…

A:

Q: L is a line in 2-space or 3-space that passes through the points A a then the distance from a point…

A:

Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

A: We have to solve given problems:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.