Consider a plane containing the point P = (-4,-4, 3), such that the vectors are parallel to the plane, as shown in the picture below: u= -1 1 2 , V = 1 -3 2 •R EL U Y X

Q: Given a vector and 2 points, A(5,–2,7) and B(9,–2,1) in a plane. (a) Find dot product of vector…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the intersection of this plane with the line…

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Q: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

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Q: Use the vector cross product to nd the equation of the plane in R3 containing the three points…

A: Points are  4,1,2,1,-1,1,5,2,3

Q: Tom is  considering purchasing a consol that promises annual payments of $4.  If the current…

A: Here, the annual payments of consol is $4 and the current interest rate is 5 %. Price of the consol…

Q: Using the same vectors v = (1,3, 2) and w = (3,5,6) and the same poin P= (8,4,-2). Find the equation…

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Q: Verify that 2j+k is perpendicular to the plane I7, Find a vector perpendicular to the plane II, Find…

A: Given that the plane Π2 contains the point O, A and B and the plane Π3 contains the points O, A and…

Q: Let P and Q be the points in R3 with position vectors p = (4, -6, 1) and q = (1, -3, -5),…

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Q: Find a unit vector v orthogonal to the plane that connects the points P = (4, 5, 2), Q = (8, 9, 6)…

A: Given that the plane that connects the points P = (4, 5, 2), Q = (8, 9, 6) and R = (8, 9, 9)

Q: ii) Determine whether u and v are orthogonal or not.

A: Let x = <a, b, c> Given :-  x with magnitude 3 is in opposite direction to u. -u =…

Q: d) Check whether the given points P(2, -3, 4), Q(-1, 2, 3), R(0, 7, 1) are collinear or not. e) Find…

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Q: Given a vector A = 3a, - 2a, - 16a, find its components normal to the plane 2x + 2y – z + 8 = 0 and…

A: We have to determine component normal to the plane

Q: Find the value of a such that the vectors a and b are perpendicular where a = a î - 16 ĵ - 19 k and…

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Q: Find the vector equation of the plane that contains the parallel lines [x, y, z]= [0,1,3] + [-6,…

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Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1).…

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Q: The plane passing through the three points A(0, 1,3), B(3,4,3) and C(2,3, –1) can be expressed as a…

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Q: Find a vector, w, which is perpendicular to the vectors where u=61-15 Ĵ + 7k and v= -19 1+53 - 5 k.…

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Q: Given two vectors a = (−2, 1, 3) and b = (3, −1, 2), does c = (−18, 7, 1) lie on the plane…

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Q: Find a unit vector perpendicular to the plane containing the points A(1, 2, 3), B(3, 2, 1), and…

A: The given plane contains the three points .Now, find the vectors .

Q: two points in the 3D plane, where A=(2,-4,6) and B=(5,-9,8). Which of the following would be the…

A: In this question, the magnitude of the vector is determined. The magnitude of the vector A→=a,b,c is…

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

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Q: Consider a plane with direction vectors  [−2,8,5] and  [5,0,−7]. The plane passes through the point…

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