Determine the general equation of the plane that passes through the point P (-1,1,0) and that has a normal vector n = (2,0, -4).

Q: Find the normal vector to the plane that contains the point (1, 1, 3) and the line r(t)=(0,1,…

A: Let P be the point 1,1,3.Q be the point 0,1,2 on the line.Then, PQ→ = 0-1,1-1,2-3=-1,0,-1And the…

Q: Determine a vector equation for hte line through the point: (-2, 0, -8) perpendicular ot the plane:…

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Q: Write the equation of the line passing through P with normal vector n in normal form and general…

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Q: A vector equation for the line through the points A (3, -4, -3) and B (3,4,2) is (x, y, z) = . (You…

A: Concept to be used:If a line passes through two points A,Bwith position vectors aand brespectively,…

Q: Find a vector v parallel to the intersection of the planes - (x + y + 3z) = 4 and 3y - 3x - z = 7.…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let P be the like (-1,0,2) . Consider the plane that goes through the points A=(3,4,-1), B=(1,-3,3)…

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Q: Is the vector parallel to the plane x+2y+z+4=0? Explain why?

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Q: Find the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

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Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: Find the intersection of the line that passes through (0,3,-1), in the direction of…

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Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: Which of the following is a normal vector to the plane which is parallel to vectors (0,−3,1) and…

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Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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Q: Determine the equation of the plane with a point 'a' and the normal vector 'n': a = (−1, 2, −3)t ,…

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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.