Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 – 2t, x3 = 4t – 5, x4 = 3t – 3, where t is a free variable. Use vectors to describe this solution set as a line in R*. L(t) =| +t

Q: Solve the following equations numerically by using the Euler algorithm and compare with the exact…

A: The given equation is

Q: Do the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane? Justify your…

A: To check: If the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane and…

Q: Write the equations of three non-parallel planes that all intersect at (-4, 7, 1).

A:

Q: The midpoint between the points (6, -7, -2) and(-2, 1, 4) is

A: The solution of the problem is given in the next step.

Q: 3x^(2)+4y^(2)+18x+18y+19=0   Find the coordinates of the latus rectum

A:

Q: axis where each point lies.

A: Given,

Q: Find the midpoint between the coordinate points (1, - 4) and (4, 0).

A: We can solve the problem by the formula of obtaining midpoint.

Q: A tunnel is being constructed through a mountain range where the tunnel is being constructed from…

A:

Q: Find the equation of the plane through (1, 0, 1), (−1, 2, 2) and (0, 0, 2).

A:

Q: ketch the surface

A:

Q: A) Write the equation of the line PARALLEL to y + 3x = -8 and passes through (6,-4) Do NOT use the…

A:

Q: 4. Express (-23+ j2) in rectangular form.

A: Let's find.

Q: Write the equation of the perpendicular bisector that goes through the line segment with end points…

A: Given: Two points A(1,2) and B(-2, 8)

Q: 2. (a) What is the negation of [Por Q]? (b) What is the negation of [P &-Q]? (c) Using the rules of…

A: Note-  Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Q3/ Give a pictorial view for the points to show its position in space: we this A-2,-4) ,B=(4,0) ,…

A: The first point A= (-2,-4) lies in the third quadrant, the second point B= (4,0) lies in first…

Q: Find the set of parallel lines intersecting at a point (3, -2, 0).

A: Use : Parallel lines never intersect.

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.