A plane P passes through the points P(3, –1, –4), E(2,7, –1), and G(-1,6, 1)

Q: Find the directed distance from the given line to the given point. (-1, 6) (5, 4) (10, 8) (1, 2)…

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Q: Suppose that Mrs. Jena (in the position of T) want to travel to the top of regions diagonally right…

A: To find the number of route to reach the top of the region :-

Q: the origin is shifted to the point (–2, 3) and the new co-ordinate axes are parallel to the original…

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Q: Find the locus of the points z that satisfies 3(22 + z?) + (8 – 16i)z + (8+ 16i)z – 10|z|? = 16.

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Q: Find the plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (3, -1, 1), (1,…

A: Data points 0,-4 , 0 ,5 , 0 ,0 ,3 , -1 , 1 ,1 , -2 ,1 ,1,-5 , -3. To Find: The plane z=a+bx+cy that…

Q: If the plane contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), W(a, 1, ), then a = -6 O-2

A: Solution: The equation of plane passing through points P1,0,0, Q3,2,0, R0,2,1 is x-y+3z-1=0

Q: Show that the points A(8,-1,0), B(0, 1, 1), and C(2, 1, -3) are non-collinear.

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Q: (c) Determine the values of a and b if T(x,y,z) = (2x+y+z,a+3y,b+4z) is not self- adjoint.

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Q: are linearly independent if and only if k # -0-2-0 v= -6 -1 + k 3 = 5 1 1 7

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: The line of intersection of the planes x + y + z = 0 and x - y = 0 is

A: The given planes are..Find the equation of the line in parametric form.

Q: Let S {X,Y.Z} be a subset of IR, where X (2.-1.1.3), Y = (2,1,-1,-3) and Z = (-4,2,1, -6). i. Is S…

A: Let the set of vectors is defined as  P={K,L,M} . The vectors, K, L, M are linearly independent, if…

Q: Q4) Determine whether the set S is linearly independent or linearly dependent a) S = {(2,1,–2),…

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Q: . Decide which of the following sets are linearly independent in R. Justify your answer in each…

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Q: 19. The plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1) Answer + -4x + 3y + z = -14

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Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: For which values of C is the set C linearly dependent? 3. C = -1, 2 C=-1,-2 C=1,-2 C= - 1, 1 O c=1,…

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Q: The Vertex and the value of p'of the given parabola (x – 4)2 = 12(y – 7) are | - Vertex = (-4, –7);…

A: Use vertex form of parabola

Q: 4. (a) Are the points u = independent? (1, 2, 3), v = (-1,0, 1) and w = (5, 4, 3) linearly (b) If…

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Q: 4. Find the equation of the plane through the given points. (a) (1,1,2), (0, 0, 1), and (-2, -3,0).…

A: We have to find equation of plane passing through given points in part a) and part b) Concept…

Q: nt of intersectic -6 y + 8 = 3 O) カー

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