Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in the form ax + by + cz = d.

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: :Find the equation of the plane through (-1 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

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Q: Let R be the parallelogram enclosed by the lines x + 3y = 0, x + 3y = 2, x + y = 1 and x + y = 4.…

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Q: Find an equation of the plane containing the three points P(1,2,2), Q(2,-1,4), and R(3,5,-2).

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Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

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Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 1,1), and R(1,1,0). Write the…

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Q: A line, in R³ which passes through the point (xo, yo, zo) and with the direction vector (a, b, c),…

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Q: Let a be a real number such that a opposit to 0 . An equation of the plane passing through A…

A: Given data:- Plane passing through the points, Aa,-a,-aBa,0,2aC-a,-a,-5a

Q: Prove that three points P(5,-4), Q(-3,8) and R(1,2) on the rectangular coordinate plane are…

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Q: :Find the equation of the plane through (-1, 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

A: Given,           The equation of the pane through -1,6,1 and perpendicular to the join            of…

Q: Let A = (1, –1, 2) and B = (4, –2, 3). Solve for proj,B. %3D

A: As per the guidelines for the multiple questions I had solved the first question.

Q: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two vector.…

Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

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Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

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.