that Let P be the point (1,0,2). Consider the plane through the points A= (3,4,-1), B= (1,-3,3) and (= (1,20). Soej Find a vector plane that goes through the point P and is parallel to the plane that goes through the points A, B and C. :) Find a point-normal equation for this plane

Q: (a) Find the equation of the plane p containing the point P (4, 3, 4) and with normal vector (2,…

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Q: 5. (a) Given A = a,5-ay2 + a₂, find the expression of a unit vector of B such that B/A and BL A, if…

A: Solution 5(a): Given that A→=5ax-2ay+az and  B→∥A→ if B→ lies in the xy-plane. So, B→=5bx-2by. Unit…

Q: Plane passing through point P0 (1, 2, 1) and perpendicular to vector (1, -1, 2) Find the equation…

A: Given:  Plane D1 : passing point P0(1, 2, 1)                 perpendicular vector (1, -1, 2) Plane…

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: Use the definition to determine whether or not =(3,5,-2)'. =(-2,1,4)', and =(1,3,7) are linearly…

A: We have to check whether given set of vector is linearly independent or dependent.

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: 8) The point A(1,2,2) is a point on the plane with normal vector n= (-1,2,6) Determine the Cartesian…

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Q: Represent the line segment from P to Q by a vector-valued function. P(4, 0, 7), Q(3, -3, 4) r(t) =…

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Q: X1 x2 x3 2 -1 3 (1)x+( + μl 2

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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: The plane with normal vector (6,-5, 1) containing the point (0,-2,3) has equation Ax+By+Cz = D. If…

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Q: Let / be the line through the point with coordinates (0,0,1) in the direction of the vector…

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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: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem

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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Q: Let /be the line through the point with coordinates (2,-1,0) in the direction of the vector G) 1…

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

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Q: Calculate the distance from point B=(−1,3,−1) to the plane that passes through point A=(3,2,−1) and…

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Q: Consider the R³ vectors v₁ = B. 3 23 V2 = 2 H -1 and v3 = D 3 (a) Find a linear dependence…

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Q: Find an equation of the plane that passes through the point Po(0, -2,3) with a normal vector n =…

A: To find the equation of a plane that passes through the point with a normal vector , you can use…