Find an equation of the plane. The plane through the point (3, 2, 3) and with normal vector 9i + j − k

Q: Consider the points below. P(3, 0, 3), Q(-2, 1, 4), R(6, 2, 5) (a) Find a nonzero vector orthogonal…

A: We need to solve plane problem.

Q: A parallel, orthogonal, or neither? 3. Find the equation of the line through the point (0, 1, 4) and…

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Q: Find the equation of the plane perpendicular to the given vector N and passing through the given…

A: Vector N = (1, 0, -5) and point is given as (5, -1, 3)

Q: 3) Find equations for the lines: a 21 g. The line through (0.-7,0) perpendicular to the plane…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

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Q: 6i + Points A, B, C, D in a plane have position vectors a 8j, b = 3a/2, c = 6i+3j, d = 5c/3…

A: Position vector of point A is: a→=6i+8j Position vector of point B is: b→=32a→=9i+12j Position…

Q: Let A = and B , P = (9, 8, 7) c. find an equation for the plane containing A and B and the point P.…

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Q: A plane that passes through the points A(2,1,1) B(-1,-1,10) C(1.3.-4). Find a vector perpendicular…

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Q: a) Find the vector component of L = along A = and orthogonal to L. b) Find the area of the triangle…

A: I am doing all parts of que 2.

Q: Fibe the graph of the equation. = (7 – 21) i + 10tj r = O It is a line in 2-space through the point…

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Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6). Q2. Find the angle between…

A: 1. Find the distance between the points A-1,3,7 and B2,-1,6. 2. Find the angle between the vectors…

Q: x- 2. Find a vector equation of a plane that contains the line y+2 -2 and the point A(1,2,1).

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Q: The vector equation of two lines , and 4 are 1+x 2- -3+2 and 4 a-y= Given that/, and /, intersect at…

A: Solution (i): Value of a Given lines are, (1+x)/2​=(2-y)/3​=(−3+z)/4​=(r1​)(say)     .... (i)So,…

Q: Given point A (6,5,8) and plane p with the equation 3x + 2y + 5z = - 24. a. Point A is on the plane…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: (A) Find the unique point P on the y-axis which is on both planes. (B) Find a unit vector u with…

A: (a) ... Unique point on the  y axis on the both planes  On the y axis means, x and z=o  Which means…

Q: Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) find the area…

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Q: d = (-4, –2) and b = (1,3). Represent ä + b using the parallelogram method. Use the Vector tool to…

A: Let us draw a line parallel to the vector a and one more line parallel to vector b.  Both intersect…

Q: passes through the point P(3,7,2) and is perpendicular to the plane 3x − 5z – 7 = 0. -

A: The given point is P3,7,2 and the given plane is 3x-5z-7=0.We need to find the vector equation of a…

Q: Equation of the plane passes through the point (1, 2, 3) and parallel to the vector A= 2i+3j :+k and…

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Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), Q(2, 0, –1), and…

A: Cross product of any two vectors gives a vector which is perpendicular to the both the given vector…

Q: The intersection of the two planes given by the vector equations r. 1 = 0 and -2 2 = -3 r. is a. a…

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Q: Let å = and b= 3 a) Find the area of the parallelogram formed by the two vectors. b) If the two…

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Q: Given the three points A(1, 3, -2), B(2, 1, –3) and C'(2, 1, –1). (a) Find the vectors AB and AĆ.…

A: Topic:- vector

Q: 2. 3. 10,6,-31 You can now find the equation of the plane that contains the point (4,-1.3) and is…

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

A: Two vectors in opposite directions that are orthogonal to the vector u  where u = 7, -6, 9 Proof:…

Q: A 1. : Two vectors, F1 = 50 N and F2 = 60 N, have directions as shown in the figure below. Determine…

A: To determine the resultant of the two vectors in the x-axis and the y-axis, first determine the…

Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

A: After solving the problem, we get only one equation. But, there is three variables. So, we have to…

Q: Find the vector equation of the plane that contains the line = [2,0,5] + t[2,-1,3] and passes…

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Q: Find a vector perpendicular to the plane that contains the points  P(1, 0, 0), Q(2, 0, −1), and…

A: Three points are given, We have to find the equation of the plane contains the given three points.…

Q: a State the condition(s) that a, b, c, and d must satisfy for the vector b to be 1 1 -1 and spanned…

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

A: Given :u=<6,-3,8>

Q: Find the requested equations below Find some symmetric equations for the line with point P(4, -4,…

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not…

A: We have to find perpendicular vector to the given vector.

Q: Given the vectors u = (1, 1,-1,-1) and v = (2, -3, 0, 6), and the point x = (-1,0,2,1) in R¹. (i)…

A: Given- Given the vectors u = 1, 1, -1, -1 and v = 2, -3, 0, 6, and the point x0 = -1, 0, 2, 1 in ℝ4.…

Q: Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously…

A: Concept: A plane going through three non-collinear points has the following equation: Vectors and…

Q: (a) Find a vector perpendicular to the plane that contains the points  P(1, 0, 0), Q(2, 0, −1),…

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Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), Q(2, 0, -1), and…

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Q: Find a non-zero vector i perpendicular to the vectors 3 -13 and i = 4

A: Given problem:-

Q: A:-Find parametric equations for the lines, the line through (4, 7, 1) perpendicular to the vectors…

A: I am attaching image so that you understand each and every step.

Q: 16. Find the vector and Cartesian equation of the planes containing, a. the point 4(1,5, 3) and…

A: Part A :-

Q: Determine the vector and cartesian equation of the plane that passes through the points ?(−3, −2,0),…

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Q: a vector equation of the line AB Cartesian equation of the line 1, passing through a and d. A…

A: According to our company, we are supposed to answer only three parts of the question(4). For the…

Q: 25. A plane passes through the point (1, 2, 3) and is perpendicular to a straight IHe IH the…

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Q: Describe the graph of the equation. r = (5 – 21) i + 11tj O It is a plane in 2-space through the…

A: In this question we have to describe graph of equation.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given that the plane is perpendicular to n=j. The direction vector of n=j is (0,1,0) So the normal…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Topic = Vector

Q: Q4) 1- Find the area of the triangle determined by the point P(1, -1, 2), Q(2, 0, -1), and R(0, 2,…

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