6. Let O be the origin and A, B, C be points in R³ such that OÀ=i+j+k - OB=31+3 OC=-1+j+k Suppose P is the plane passing through O, A, B. (a) Find a non-zero vector which is perpendicular to the plane P. (h) Find the proiectis

Q: A plane in R³ contains the point (-r, 0, 1) and has the vector (1,4,3r) as a normal, where r is a…

A: Explained above in detail.

Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

A:

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: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: A plane in R'is perpendicular to the vector (4, 2, – 9), and contains the point (- 9, 5, - 8). Find…

A: A plane in ℝ3 is perpendicular to the vector 4, 2, -9 and contains point -9, 5, -8To find the…

Q: Let A be the plane containing the points P(2,2,2), Q(2, 1,3 ) and R(3,1, 3) . (a) Find the equation…

A:

Q: e) Plane that is parallel to the xy-plane that contains the point A(2, 1, 3) (ca

A:

Q: 4. Consider the vectors u,v and w are defined, u = 3i-j+4k, v = 4i – 2j +6k and w= 5i+2k (a) Express…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. A scalar equation of the plane with normal vector = [0, -1, 3] and passing through the - point…

A: Topic = Geometry Correct option = A

Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

A:

Q: B 10. Write a vector equation and parametric equations for a plane that satisfies each set of…

A: Due to Bartleby answering guidelines I have solved only first three Subparts of the given question…

Q: 8. Determine a vector equation for the plane with Cartesian equation: 2x -y + 3z-24 = 0

A:

Q: A plane intersects the a1, a2 and a3 axes at 0.2, 0.1, and -0.5. The reciprocal vector perpendicular…

A: If the Miller indices for a plane is h k l , then the reciprocal vector normal to the plane is…

Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

A: Note:  part(b) is the independent subpart of part(a) and also it is incomplete. so part (b) can't be…

Q: 2. The four points P(3, 1, 2), Q(1,0, 2), R(2, 1,0) and T(1, 1,-2) in R' lie on the same plane. (a)…

A:

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: 3.Vector (3, −7, 5) is normal to a plane P and point (0, 0, −2) is in the plane. Provide equation of…

A:

Q: 2. (6 marks) Find the vector equation of a plane a) Passing through the point A(-1, 2, -3) and…

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Q: Let A be the point with coordinates (5, 2, 3) and let B be the point with coordinates (4, 2, 3). Let…

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Q: QUESTION 6 Let fo(x) = nx2 +5 for neN and x ER 4n +3 1. Show that (f.(x)) converges uniformly on [ -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let L be the line passing through the point P(1, -1, -2) with direction vector d=[3, −4, 0]T, and…

A:

Q: Let P be a plane in R3 given in vector form by -> x = td + sd, +p and l be a line in R3 given in…

A: Given that D:x=td1+3d2+p is the plane passing through the point whose position vector is P and…

Q: r(u)=(a1u2+b1u+c1,a2u2+b2u+c2,a3u2+b3u+c3), u∈R lies in a plane, and find an equation of the plane.

A: Given:r(u)=a1u2+b1u+c1, a2u2+b2u+c2, a3u2+b3u+c3To find:The equation of the plane.