A(6,3,3), B(3,5,1) and C(-1,3,5)are the point in a three-dimensional space. Find,a) The vector BA and BC in terms of i, j,k. Hence, show that BA is perpendicularto BC.b) A unit vector that is perpendicular to plane containing the point A, B and C.c) A Cartesian equation of the plane described in (b).

Answered: A(6,3,3), B(3,5,1) and C(-1,3,5)are the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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5. Find a) The position vector in the form of xr + yr for the vector that starts at the point (-1, 2), and ends at the point (10, -7). b) The magnitude and direction of the vector found in part (a)
If a line is parallel to the vector 6?+6?+9?6i+6j+9k and passes through the point ?=(3,2,1)P=(3,2,1), then the parametric equation of the line is : a. X=3+ 6λ, Y= 2+ 6λ, Z= 1+9λ b. X=-3-6λ, Y=- 2- 6λ, Z= -1-9λ c. X=3-6λ, Y= 2- 6λ, Z= 1-9λ d. X=-3+ 6λ, Y= -2+ 6λ, Z= -1+9λ
a) Accurately sketch the position vector OQ=(-3, 5,4) using a rectangular prism b) label each of the vertices of your prism with its co-ordinates use 3 colors one for axes one for the prism and one for your vector write an equation for the plane containing the top of your prism
only do 12
1. Given the points P(3, 7, -5), Q(4, -9, 0) and R(6, 9, -4), determine each of the following equations and write your final answers below in the specified form. a) the equation of the line through P and Q. b) the equation of the plane through P, Q, & R. [vector] [parametric] [vector] [symmetric] [Cartesian/Scalar]
Please solve 1a)-1d) a)Calculate the following equation considering the vectors, a=(4,-2,-4), b=(1,6,7) and c= (1,-1,-2). (ax b) - (a x c) b) For the vectors a = (2,-1,-3) and b = (3,-4,2), calculate the scalar proj, a and scalar proj b. State both projections in scalar form. Explain and discuss what vector projection of two vectors are. You may use a diagram to help with this explanation. Be sure to discuss the cases of different angles. c) Calculate the following equation considering the vectors, a=(2,-1,3), b=(4,1,-2) and c= (8,3,-1). d)
=(2,3,1) Determine the vector equation and the Cartesian equation of line 1₁ passing by points A = and B = (0, 0, 1) and line 1₂ passing by points C (0, 0, 0) and D = (4, 6, 0). Demonstrate that the lines ₁ and 2 are coplanar. = In case they are coplanar, obtain the vector equation and the Cartesian equation of the plane they belong to.
Write the equation of the plane with normal vector n passing through point Po in the scalar form ax + by + cz = d. n = (-3,7,9), Po = (4,5,3) (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation of the plane:
Let vector a=4i-5j+3k and a point P(2,-1,3). If the length of PQ is equal to the length of vector a, and vector PQ is opposite to vector a, then the coordinate of Q is … (2,-4,0) (6,-6,0) (-2,4,0) (6,-6,-6) The equation for the plane passing through points (3,2,1),(2,1,-1), and (-1,3,2) is given as follows. 9x + y - z - 16 = 0 x + 9y - 5z - 16 = 0 x - 9y - 5z + 16 = 0 x + 5y - 9z - 16 = 0choose the correct answer

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