50. Find the vector from the origin to the point of intersection of the medians of the triangle whose vertices are А(1, -1, 2), В(2, 1, 3), and C(-1, 2, -1).

Q: Find the vector in R³ from point A = (–4, 7, 6) to B = (–8, –5, 7). AB: =

A:

Q: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

Q: Q1: suppose the middle of each side of the triangle is a vector from the vertex (1,2,3), (3,2,1),…

A: Vectors

Q: Add the vectors E = , F=, G .

A:

Q: Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

A: topic - vectors

Q: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

A:

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: plot the given pair on a cartesian plane {(1,1),(2,4),(3,7),(4,10),(5,13)}

A: The given pair of points are  A(1,1), B(2,4), C(3,7), D(4,10), E(5,13)

Q: Show that the vectors (1,0,1); (-1,2,3) and (0, 1; -1) spans R³

A:

Q: Consider the vectors i = (6,4), i = (-2,6), = (4, 2), and i = (-2, 3). Which of these vectors are…

A:

Q: Write a vector equation for the line segment from (-3, 0, 0) to (0, 4, 3).

A: To write a vector equation for the line segment from -3, 0, 0 to 0, 4, 3. To write a vector equation…

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: Draw the vectors in standard position in R2 with their tails at the point (2, -3).

A:

Q: Sketch the vectors = (2, 3,-6) and w = (-1,1,1) and draw -U, v + w and 7 - w.

A: The given vectors are

Q: 16. Determine the vector equation of each line.

A: Given details for each lines are :(a) Parallel to y axis and passes through (b) Perpendicular to…

Q: 17) Let a = [3, -4] and b = [−6, k]. a) Determine the value(s) of k such that a + b = a + 6. What is…

A:

Q: Find the vector equation of the line (d) through (6, −3) and parallel to the line through (5, −1)…

A: First, we find the slope of the line  through (5, −1) and (2, 11) Direction vector is=(2, 11)-(5,…

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.