(a) The line lı passes through the point A (0, 1, 2) and is perpendicular to the plane x - 4y - 3z= 0. Find the Cartesian equations of l1. (b) The line 2 is parallel to li and passes through the point P(3, –8, –11). Find the vector equation of the line l2.

Q: 2. Find an equation (parametric and vector form) of the line if the line is perpendicular to the…

A:

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –6) + t(1,…

A:

Q: Consider the points A(-3, 4, 2) and B (8,-1, 5). (a) (i) Find AB. () Find AB (ii) 2 1 A line L has…

A:

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: 5. Determine a vector equation of the line that passes through the origin and is parallel to the…

A: Determine a vector equation of the line that passes through the origin and is parallel to the line…

Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: 1. Determine whether the points A(3,4,-1) and B(1,-1,0) lie on the line with vector equation…

A: Given vector equation :

Q: Find the B-coordinate vector fe

A: First multiply some constant with given coordinator polynomial and equal the vector p(t) and find…

Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

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.